Quartz crystal unit, quartz crystal oscillator and electronic apparatus

ABSTRACT

A quartz crystal unit comprises a quartz crystal tuning fork resonator having a quartz crystal tuning fork base, and first and second quartz crystal tuning fork arms. Each of the first and second quartz crystal tuning fork arms has a first main surface and a second main surface opposite the first main surface, and at least one groove formed in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork arms. At least one mounting arm having a width less than 0.45 mm protrudes from the quartz crystal tuning fork base, and the overall length of the quartz crystal tuning fork resonator is less than 2.1 mm.

FIELD OF THE INVENTION

The present invention relates to a resonator, a unit having theresonator, an oscillator having the unit and an electronic apparatushaving the oscillator, and their manufacturing methods.

BACKGROUND OF THE INVENTION

There are many electronic apparatuses comprising a display portion and aquartz crystal oscillator at least. For example, cellular phones,wristwatches, facsimiles, digital cameras and DVD recorders comprising aquartz crystal oscillator are well known. Recently, because of highstability for frequency, miniaturization and the light weight nature ofthese electronic apparatuses, the need for an electronic apparatuscomprising a smaller quartz crystal oscillator with a frequency of highstability has arisen. For example, the quartz crystal oscillator havinga quartz crystal tuning fork resonator housed in a unit, which vibratesin a flexural mode, is widely used as a time standard in an electronicapparatus such as the cellular phones, the wristwatches, the facsimiles,the digital cameras and the DVD recorders.

Similar to this, the same need has also arisen for an electronicapparatus comprising a contour mode resonator such as alength-extensional mode quartz crystal resonator, a width-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonatoror a thickness shear mode quartz crystal resonator or a SAW (SurfaceAcoustic Wave) resonator or a resonator for sensing angular velocitymade of a piezoelectric material such as quartz crystal, lithiumtantalite (LiTaO₃), lithium niobate (LiNbO₃) and ceramics.

Heretofore, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aminiature quartz crystal tuning fork resonator of the prior art, capableof vibrating in a flexural mode, and having a frequency of highstability, a small series resistance and a high quality factor. This isthe reason why, when miniaturized, the quartz crystal tuning forkresonator of the prior art, capable of vibrating in a flexural mode hasa smaller electromechanical transformation efficiency. As a result, theresonator has a frequency of low stability, a large series resistanceand a reduced quality factor.

Additionally, there has been a big problem in the quartz crystaloscillator of the prior art having the quartz crystal tuning forkresonator of the prior art, such that a frequency of a fundamental modeof vibration of the tuning fork resonator which is an output signal ofthe oscillator jumps to a second overtone mode of vibration thereof byshock or vibration.

Similarly, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with a contourmode resonator such as a length-extensional mode quartz crystalresonator, a width-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator or a thickness shear mode quartz crystalresonator or a SAW resonator or a resonator for sensing angular velocityhaving a frequency of high stability, a small series resistance and ahigh quality factor because, when miniaturized, each resonator has asmall electromechanical transformation efficiency, as a result, afrequency of low stability, a large series resistance and a low qualityfactor, and also is not strong against shock.

It is, therefore, a general object of the present invention to provideembodiments of a quartz crystal resonator, a quartz crystal unit, aquartz crystal oscillator and an electronic apparatus of the presentinvention, which overcome or at least mitigate one or more of the aboveproblems.

SUMMARY OF THE INVENTION

The present invention relates to a resonator, a unit, an oscillator andan electronic apparatus comprising a display portion and a plurality ofoscillators, one of which comprises a quartz crystal oscillatorcomprising a quartz crystal oscillating circuit having an amplificationcircuit and a feedback circuit, and also relates to their manufacturingmethods, and in particular, relates to a quartz crystal resonatorcapable of vibrating in a flexural mode, a quartz crystal unit havingthe quartz crystal resonator and a quartz crystal oscillator having thequartz crystal unit and having an output signal of a frequency of highstability for a fundamental mode of vibration of the quartz crystalresonator, and also to a quartz crystal oscillator having a suppressedsecond overtone mode of vibration of the quartz crystal resonator, inaddition, relates to a quartz crystal oscillator comprising an anothercontour mode resonator such as a length-extensional mode resonator, awidth-extensional mode resonator and a Lame mode resonator or athickness shear mode resonator, each made of quartz crystal or a SAWresonator or a piezoelectric resonator for sensing angular velocity. Thequartz crystal oscillator is, therefore, available for the electronicapparatus requiring a miniature quartz crystal oscillator with high timeaccuracy and shock proof.

It is an object of the present invention to provide a miniature quartzcrystal resonator, capable of vibrating in a flexural mode, and having ahigh electromechanical transformation efficiency.

It is an another object of the present invention to provide a miniaturequartz crystal unit with a quartz crystal resonator, capable ofvibrating in a fundamental mode of vibration of a flexural mode, andhaving a high electromechanical transformation efficiency.

It is a further object of the present invention to provide a quartzcrystal oscillator with a miniature quartz crystal resonator, capable ofvibrating in a flexural mode, and having a frequency of high stability,a small series resistance R₁ and a high quality factor Q₁, whose nominalfrequency for a fundamental mode of vibration is within a range of 10kHz to 200 kHz. Especially, a frequency of about 32.768 kHz is veryavailable for a time standard of a frequency signal.

It is a still another object of the present invention to provide anelectronic apparatus comprising a display portion and a plurality ofoscillators.

According to one aspect of the present invention, there is provided aquartz crystal resonator comprising: a plurality of vibrational arms,each of the vibrational arms having a first main surface and a secondmain surface and side surfaces; and a base portion to which thevibrational arms are attached, in which the resonator has apiezoelectric constant e′₁₂ in the range of 0.1 C/m² to 0.19 C/m² in theabsolute value.

According to a second aspect of the present invention, there is provideda quartz crystal unit comprising: a quartz crystal resonator having abase portion and a plurality of vibrational arms attached to the baseportion; a case for housing the quartz crystal resonator; and a lid forcovering an open end of the case, each of the vibrational arms having afirst main surface and a second main surface opposite the first mainsurface and side surfaces, in which the quartz crystal resonator has acutting angle in the range of ZYlwt(−20° to +20°)/(−25° to +25°)/(−18°to +18°) and a piezoelectric constant e′₁₂ of the resonator is within arange of 0.1 C/m² to 0.19 C/m² in the absolute value.

According to a third aspect of the present invention, there is provideda quartz crystal oscillator comprising: a quartz crystal oscillatingcircuit comprising; an amplification circuit comprising a CMOS inverterand a feedback resistor, and a feedback circuit comprising a quartzcrystal resonator capable of vibrating in a flexural mode, a pluralityof capacitors and a drain resistor, the quartz crystal resonator beinghoused in a package comprising a case for housing the quartz crystalresonator and a lid for covering an open end of the case, andcomprising: a plurality of vibrational arms, each of the vibrationalarms having a first main surface and a second main surface opposite thefirst main surface and side surfaces; and a base portion to which thevibrational arms are attached, in which the quartz crystal resonator hasa cutting angle in the range of ZYlwt (−20° to +20°)/(−25° to+25°)/(−18° to +18°) and a piezoelectric constant e′₁₂ of the resonatoris within a range of 0.1 C/m² to 0.19 C/m² in the absolute value.

According to a fourth aspect of the present invention, there is providedan electronic apparatus comprising a display portion and a plurality ofoscillators, one of the oscillators being a quartz crystal oscillatorcomprising: a quartz crystal oscillating circuit comprising; anamplification circuit having a CMOS inverter and a feedback resistor,and a feedback circuit having a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode of an inverse phase, a pluralityof capacitors and a drain resistor, the quartz crystal tuning forkresonator comprising a tuning fork base and a plurality of tuning forkarms connected to the tuning fork base, each of the tuning fork armshaving a first main surface and a second main surface opposite the firstmain surface and side surfaces, the quartz crystal tuning fork resonatorbeing housed in a package comprising a case for housing the resonatorand a lid for covering an open end of the case, in which the quartzcrystal tuning fork resonator has a fundamental mode of vibration and asecond overtone mode of vibration and the amplification circuit of thequartz crystal oscillating circuit has negative resistances −RL₁ and−RL₂ for the fundamental mode of vibration and the second overtone modeof vibration of the quartz crystal tuning fork resonator, in which anabsolute value of the negative resistances is defined by |−RL₁| and|RL₂| and a ratio of the |−RL₁| and R₁ is greater than that of the|−RL₂| and R₂, where R₁ and R₂ represent a series resistance of thefundamental mode of vibration and the second overtone mode of vibrationof the quartz crystal resonator, respectively, in which an output signalof the quartz crystal oscillating circuit has an oscillation frequencyof the fundamental mode of vibration of the quartz crystal tuning forkresonator and is a clock signal which is used to display time at adisplay portion of the electronic apparatus, and in which the quartzcrystal tuning fork resonator has a cutting angle in the range of ZYlwt(−20° to +20°)/(−25° to +25°)/(−18° to +18°) and a piezoelectricconstant e′₁₂ of the resonator is within a range of 0.1 C/m² to 0.19C/m² in the absolute value.

Preferably, the piezoelectric constant e′₁₂ is within a range of 0.12C/m² to 0.19 C/m² in the absolute value.

Preferably, mounting arms protruding from the base portion comprise two.

Preferably, each of the vibrational arms has a groove having a firststepped portion and a second stepped portion.

Preferably, each of the vibrational arms has a through groove.

Preferably, a merit value M₂ of a second overtone mode of vibration ofthe quartz crystal resonator having vibrational arms and a base portionis less than 30.

Preferably, the quartz crystal oscillator with the quartz crystalresonator is constructed so that a ratio of an amplification rate α₁ ofthe fundamental mode of vibration and an amplification rate α₂ of thesecond overtone mode of vibration of the amplification circuit isgreater than that of a feedback rate β₂ of the second overtone mode ofvibration and a feedback rate β₁ of the fundamental mode of vibration ofthe feedback circuit, and a product of the amplification rate α₁ and thefeedback rate β₁ of the fundamental mode of vibration is greater than 1.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a general view of a quartz crystal plate from which a quartzcrystal resonator of the present invention is formed;

FIG. 2 shows a plan view of a quartz crystal resonator of a firstembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 3 shows an A-A′ cross-sectional view of the vibrational arms of thequartz crystal resonator in FIG. 2;

FIG. 4 shows an A-A′ cross-sectional view of another embodiment of thevibrational arms of the quartz crystal resonator in FIG. 2;

FIG. 5 shows a plan view of a quartz crystal resonator of a secondembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 6 shows a plan view of a quartz crystal resonator of a thirdembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 7 shows a B-B′ cross-sectional view of the vibrational arms of theresonator in FIG. 6;

FIG. 8 shows a plan view of a quartz crystal resonator of a fourthembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 9 shows a plan view of a quartz crystal resonator of a fifthembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 10 shows a plan view of a quartz crystal resonator of a sixthembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 11 shows a plan view of a quartz crystal resonator of a seventhembodiment of the present invention, and comprising a quartz crystaltuning fork resonator capable of vibrating in a flexural mode;

FIG. 12 shows a plan view of a width-extensional mode quartz crystalresonator constructing an electronic apparatus of the present invention;

FIG. 13( a) and FIG. 13( b) show a plan view of a thickness shear modequartz crystal resonator constructing an electronic apparatus of thepresent invention and a F-F′ sectional view of the resonator;

FIG. 14 shows a plan view of a Lame mode quartz crystal resonatorconstructing an electronic apparatus of the present invention;

FIG. 15( a) and FIG. 15( b) show a plan view of a resonator for sensingangular velocity constructing an electronic apparatus of the presentinvention and a G-G′ sectional view of the resonator;

FIG. 16( a) and FIG. 16( b) show a plan view of a quartz crystalresonator of an eighth embodiment of the present invention andcomprising a quartz crystal tuning fork resonator, and a J-J′ sectionalview of the resonator;

FIG. 17 shows a plan view of a quartz crystal unit of a first embodimentof the present invention and omitting a lid;

FIG. 18 shows a plan view of a quartz crystal unit of a secondembodiment of the present invention and omitting a lid;

FIG. 19 shows a cross-sectional view of a quartz crystal unit of a thirdembodiment of the present invention;

FIG. 20 shows a cross-sectional view of a quartz crystal oscillator of afirst embodiment of the present invention;

FIG. 21 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator of the presentinvention;

FIG. 22 shows a diagram of the feedback circuit of FIG. 21; and

FIG. 23 shows a block diagram of an embodiment of an electronicapparatus of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 is a general view of a quartz crystal plate 1 from which a quartzcrystal resonator of the present invention is formed, and particularly,a relationship of cutting angles θ_(x), θ_(y) and θ_(z) of the quartzcrystal plate 1 and its coordinate system is illustrated in FIG. 1. Thecoordinate system has original point o, electrical axis x, mechanicalaxis y and optical axis z of quartz crystal and o-xyz is constructed.

First, a quartz crystal plate perpendicular to z axis, so called, Zplate quartz crystal is taken. The Z plate quartz crystal has adimension of Width W₀, length L₀ and thickness T₀ corresponding to arespective direction of x, y and z axes.

Next, this Z plate quartz crystal is, first, rotated with an angle θ_(y)about the y axis, second, rotated with an angle θ_(x) about x′ axiswhich is a new axis of the x axis, and third, rotated with an angleθ_(z) about z″ axis which is a new axis of the z axis. In this case,each of the x, y and z axes changes to x″, y″ and z″ axes, respectively,because each axis is rotated twice about two axes. A quartz crystalresonator of the present invention is, therefore, formed from the quartzcrystal plate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the quartz crystal resonator of the present invention can beexpressed by ZYlwt(θ_(y))/(θ_(x))/(θ_(z)), and each of the angles θ_(y),θ_(x), θ_(z) will be described later in detail according to resonatorsof the present invention.

FIG. 2 shows a plan view of a quartz crystal resonator 10 of a firstembodiment of the present invention and which is a quartz crystal tuningfork resonator. The resonator 10 comprises vibrational arms 20 and 31and a base portion 40 attached to the vibrational arms, and the baseportion 40 has mounting arms 36 and 37 protruding from the base portion,each of which is mounted on a mounting portion of a package comprising acase for housing the resonator and a lid for covering an open end of thecase. In addition, each of the vibrational arms 20 and 31 has a firstmain surface and a second main surface opposite the first main surfaceand side surfaces, and the vibrational arms 20 and 31 have grooves 21and 27, respectively, each of which has stepped portions comprising afirst stepped portion and a second stepped portion. Also, the resonator10 has cutting angles θ_(y), θ_(x) and θ_(z) which are within a range of−20° to +20°, −25° to +25° and −18° to +18°, respectively, namely, acutting angle of the resonator is within a range of ZYlwt(−20° to+20°)/(−25° to +25°)/(−18° to)+18°. In this embodiment, the quartzcrystal tuning fork resonator can vibrate in a flexural mode of afundamental mode of an inverse phase, and which is one of a contour modequartz crystal resonator.

In more detail, the groove 21 is constructed to include a portion of acentral linear line 41 of the arm 20, and the groove 27 is similarlyconstructed to include a portion of a central linear line 42 of the arm31. Each of the grooves 21 and 27 has a width W₂, and the width W₂including a portion of the central linear lines 41 and 42, is preferablebecause a large moment of inertia occurs at the arms 20 and 31 and thearms can vibrate in a flexural mode easily. As a result, the quartzcrystal tuning fork resonator capable of vibrating in a fundamental modecan be obtained with a small series resistance R₁ and a high qualityfactor Q₁.

In addition, when each of the vibrational arms 20 and 31 has part widthsW₁ and W₃, an arm width W of the arms 20 and 31 has a relationship ofW=W₁+W₂+W₃, and the part widths W₁ and W₃ are constructed so that W₁≧W₃or W₁<W₃. In addition, the width W₂ is constructed so that W₂≧W₁, W₃. Inthis embodiment, also, the grooves are constructed at the arms so that aratio W₂/W of the width W₂ and the arm width W is greater than 0.35 andless than 1, preferably, within a range of 0.35 to 0.95 and a ratio t₁/tis less than 0.79, where t₁ and t are a thickness of the groove and thevibrational arms, as shown in FIG. 3, to obtain a very large moment ofinertia of the vibrational arms. That is, the quartz crystal tuning forkresonator, capable of vibrating in the fundamental mode, and having afrequency of high stability can be provided with a small seriesresistance R₁, a high quality factor Q₁ and a small capacitance ratio r₁because it has a very large electromechanical transformation efficiency.

Likewise, each of the vibrational arms 20 and 31 has a length L and eachof the grooves 21 and 27 has a length l₀ (not shown here). In thisembodiment, a ratio of the length l₀ and the length L is within a rangeof 0.3 to 0.8 to get a quartz crystal tuning fork resonator with seriesresistance R₁ of a fundamental mode of vibration smaller than seriesresistance R₂ of a second overtone mode of vibration. In other words,the length l₀ is within a range of 30% to 80% to the length L. Ingeneral, the length l₀ is greater than 0.25 mm and less than 1.26 mm,preferably, within a range of 0.3 mm to 0.45 mm, or within a range of0.45 mm to 1.25 mm, more preferably, within a range of 0.45 mm to 0.51mm. Also, when a plurality of grooves are formed in at least one ofupper and lower faces of the arms and divided in the length direction ofthe arms, the length l₀ is a total length of the grooves. Like this, thelength L of each of the vibrational arms 20 and 31 and the length l₀ ofeach of the grooves 21 and 27 are determined so that the seriesresistance R₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the series resistance R₂ of thesecond overtone mode of vibration thereof. However, this invention isnot limited to this, but the quartz crystal tuning fork resonator ofthis invention may include determining the length L of each of thevibrational arms 20 and 31 and the length l₀ of each of the grooves 21and 27 so that the series resistance R₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is greater thanthe series resistance R₂ of the second overtone mode of vibrationthereof or may include determining an overall length of each of thevibrational arms 20 and 31 and the length l₀ of each of the grooves 21and 27 so that the series resistance R₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is less or greaterthan the series resistance R₂ of the second overtone mode of vibrationthereof.

In addition, electrodes 25 and 26 are disposed on side surfaces of thevibrational arm 20 and an electrode 23 is disposed on a surface of thegroove 21, which extends on a surface of the mounting arm 36 having aconnecting portion 34. Similar to this, electrodes 32 and 33 aredisposed on side surfaces of the vibrational arm 31 and an electrode 29is disposed on a surface of the groove 27, which extends on a surface ofthe mounting arm 37 having a connecting portion 35. Each of theconnecting portions 34 and 35 has a length L₂ and a width W_(S), andeach of the mounting arms has a length L₃ and a width W₆. Also, theelectrode 23 is connected to the electrodes 32 and 33, and the electrode29 is connected to the electrodes 25 and 26.

In this embodiment, the length l₀ of the groove corresponds to a lengthl_(d) of the electrode disposed inside each of the grooves, when thelength l_(d) of the electrode is less than the length l₀ of the groove,namely, the length l₀ is of the length l_(d) of the electrode. Inaddition, the base portion 40 has a length L₁ and a width W_(H), thelength L₁ is less than 0.5 mm, preferably, within a range of 0.015 mm to0.49 mm, more preferably, within a range of 0.015 mm to 0.205 mm orwithin a range of 0.12 mm to 0.45 mm, and an overall length L_(t)(=L+L₁) in this embodiment is less than 2.1 mm, preferably, within arange of 0.65 mm to 1.3 mm or within a range of 0.8 mm to 1.95 mm, morepreferably, within a range of 1.02 mm to 1.95 mm to obtain a miniaturequartz crystal resonator. Also, when a spaced-apart distance W₄ betweenthe vibrational arms is taken, a total width W₅ (=2W+W₄) is less than0.53 mm, preferably, within a range of 0.15 mm to 0.52 mm, and the widthW₅ is equal to or less than the W_(H) which is less than 0.55 mm,preferably, within a range of 0.15 mm to 0.53 mm.

In addition, the length L₃ is greater than or equal to the length L₂ andalso, the length L₁ is greater than or equal to the length L₂ or thelength L₁ is less than the length L₂. In actual, a value of L₁−L₂ iswithin a range of −0.1 mm to 0.32 mm, preferably, within a range of −0.1mm to 0.195 mm or within a range of 0 mm to 0.3 mm, more preferably, 0mm, namely, L₁=L₂, especially, when W_(H) is greater than W₅, a distanceL₄ between an edge of the connecting portion and an outer edge of thevibrational arm is within a range of 0.012 mm to 0.38 mm, preferably,within a range of 0.04 mm to 0.26 mm or within a range of 0.07 mm to 0.3mm.

In addition, the base portion 40 has a plurality of cut portions havinga first cut portion (not shown here) and a second cut portion (not shownhere), each of the first and second cut portions is cut into the baseportion 40 from a side surface having the distance L₄ between the edgeof the connecting portion and the outer edge of the vibrational arm.Namely, the first cut portion is cut into the base portion 40 from theside surface having the distance L₄ between the edge of the connectingportion 34 and the outer edge of the vibrational arm 20 and the secondcut portion is cut into the base portion 40 from the side surface havingthe distance L₄ between the edge of the connecting portion 35 and theouter edge of the vibrational arm 31.

In more detail, the base portion 40 has a first side surface and asecond side surface opposite the first side surface, the first cutportion is cut into the base portion 40 from an arbitrary position ofthe first side surface of the base portion 40 and the second cut portionis cut into the base portion 40 from an arbitrary position of the secondside surface of the base portion 40, preferably, the first cut portionand the second cut portion are formed symmetrical to an central linearline (portion) of the base portion 40. Namely, the first cut portion isformed opposite the second cut portion in the width direction of thebase portion 40. It is needless to say that the vibrational arms 20, 31are connected to a side surface of the base portion 40 different fromeach of the first and second side surfaces of the base portion 40.

In other words, the base portion 40 has first and second base portionseach including the width W_(H) and two cut portions having the first andsecond cut portions are formed between the first and second baseportions of the base portion 40. In addition, each of the vibrationalarms 20, 31 is connected to the first base portion of the base portion40 and each of the connecting portions 34, 35 is connected to the secondbase portion of the base portion 40. Namely, a third base portion havinga width less than the width W_(H) of each of the first and second baseportion of the base portion 40 is formed between the first and secondbase portions thereof. In other words, the first base portion isconnected to the second base portion through the third base portion, andthe mounting arm 36 is connected to the second base portion of the baseportion 40 through the connecting portion 34 and the mounting arm 37 isconnected to the second base portion of the base portion 40 through theconnecting portion 35 so that the second base portion of the baseportion 40 and the connecting portions 34, 35 have a U-shape or aconcave shape with the mounting arms 36, 37.

In order to get the quartz crystal tuning fork resonator having noenergy loss caused by vibration, the width of the third base portion ofthe base portion 40 is within a range of 0.06 mm to 0.32 mm, preferably,within a range of 0.08 mm to 0.28 mm and a length of the third baseportion of the base portion 40 is greater than 0.01 mm, preferably,within a range of 0.015 mm to 0.13 mm, more preferably, within a rangeof 0.02 mm to 0.12 mm.

As is shown in FIG. 2, each of the mounting arms 36, 37 extendssubstantially parallel to the vibrational arms 20, 31. However, thepresent invention is not limited to this, but includes the mounting arms36, 37 each having at least one arm portion extending not parallel tothe vibrational arms 20, 31, e.g., each of the mounting arms 36, 37 hasa plurality of arm portions including first, second, third, fourth andfifth arm portions, and each of the first, third and fifth arm portionsof each of the mounting arms 36, 37 extends substantially parallel tothe vibrational arms 20, 31, and besides the first arm portion isconnected to the third arm portion through the second arm portionextending not parallel to the vibrational arms 20, 31 and the third armportion is connected to the fifth arm portion through the fourth armportion extending not parallel to the vibrational arms 20, 31 so that adirection of the second arm portion extending not parallel to thevibrational arms 20, 31 is different from that of the fourth arm portionextending not parallel to the vibrational arms 20, 31.

Moreover, a width of the fifth arm portion of each of the mounting arms36, 37 is greater than a width of the first arm portion of thecorresponding one of the mounting arms 36, 37 and a length of the fiftharm portion of each of the mounting arms 36, 37 is greater than or equalto a length of the first arm portion of the corresponding one of themounting arms 36, 37. As shown in FIG. 2, the vibrational arm 20 adjoinsthe mounting arm 36 and the vibrational arm 31 adjoins the mounting arm37, therefore, a spaced-apart distance between the vibrational arm 20and the fifth arm portion of the mounting arm 36 is greater than aspaced-apart distance between the vibrational arm 20 and the third armportion of the mounting arm 36, while a spaced-apart distance betweenthe vibrational arm 31 and the fifth arm portion of the mounting arm 37is greater than a spaced-apart distance between the vibrational arm 31and the third arm portion of the mounting arm 37. In addition, a case ora lid has first and second mounting portions, and the fifth arm portionof the mounting arms 36 is mounted on the first mounting portion of thecase or the lid by a conductive adhesive and the fifth arm portion ofthe mounting arm 37 is mounted on the second mounting portion of thecase or the lid by a conductive adhesive.

In this embodiment, accordingly, the first arm portion of the mountingarm 36 is connected to the second base portion of the base portion 40through the connecting portion 34 and the first arm portion of themounting arm 37 is connected to the second base portion of the baseportion 40 through the connecting portion 35 so that the second baseportion of the base portion 40 and the connecting portions 34, 35 have aU-shape or a concave shape with the first arm portions of the mountingarms 36, 37.

As described above, a part or all of each of the mounting arms 36, 37extends substantially parallel to the vibrational arms 20, 31, andbesides, the mounting arm 36 is connected to the second base portion ofthe base portion 40 through the connecting portion 34 and the mountingarm 37 is connected to the second base portion of the base portion 40through the connecting portion 35 so that the second base portion of thebase portion 40 and the connecting portions 34, 35 have a U-shape or aconcave shape with the parts or all of the mounting arms 36 and 37. Itis, therefore, obvious from this that the connecting portion 34 and thefirst arm portion of the mounting arm 36 have a L-shape in a top view ofFIG. 2, and also, the connecting portion 35 and the first arm portion ofthe mounting arm 37 have a L-shape in a bottom view of FIG. 2.

Moreover, the second base portion of the base portion 40 has aconnecting portion through which the quartz crystal tuning forkresonator is connected to a quartz crystal wafer and the quartz crystaltuning fork resonator is chipped (cut off) from the quartz crystal waferat the connecting portion of the second base portion of the base portion40. Also, the second base portion of the base portion 40 has a pluralityof different lengths including a first length less than or equal to alength of the first base portion of the base portion 40, and a secondlength greater than the first length.

In addition, a corner of the fifth arm portion of each of the mountingarms 36, 37 is chamfered (cut) so that the fifth arm portion of each ofthe mounting arms 36, 37 has a plurality of different widths including afirst width and a second width greater than the first width, and aportion which has the second width of the fifth arm portion of each ofthe mounting arms 36, 37 is mounted on the corresponding one of thefirst and second mounting portions of the case or the lid by aconductive adhesive.

In this embodiment, each of the mounting arms 36, 37 has five armportions, but, may have at least three arm portions including a firstarm portion extending substantially parallel to the vibrational arms 20,30 and connected to the quartz crystal tuning fork base through aconnecting portion, a second arm portion extending not parallel to thevibrational arms 20, 30, and a third arm portion extending substantiallyparallel to the vibrational arms 20, 30 and connected to the first armportion through the second arm portion, a length of the third armportion of each of the mounting arms 36, 37 is greater than or equal toa length of the first arm portion of the corresponding one of themounting arms 36, 37, and the third arm portion of each of the mountingarms 36, 37 is mounted on a mounting portion of a case or a lid througha conductive adhesive. As a result, the quartz crystal tuning forkresonator is obtained with no energy loss caused by vibration and a lowseries resistance R₁.

In addition, each of the vibrational arms 20, 31 comprises a pluralityof vibrational portions having a first vibrational portion including agenerally tapered shape comprised of a plurality of different widthshaving a first width and a second width less than the first width, and asecond vibrational portion including a third width less than or equal tothe first width, the first vibrational portion of each of thevibrational arms 20, 31 has a first main surface and a second mainsurface opposite the first main surface, and a groove is formed in eachof the first and second main surfaces of the first vibrational portionof each of the vibrational arms 20, 31 and a width of the groove formedin each of the first and second main surfaces of the first vibrationalportion of each of the vibrational arms 20, 31 is less than 0.07 mm,preferably, greater than 0.01 mm and less than 0.05 mm, more preferably,within a range of 0.025 mm to 0.049 mm in the same way as the width ofthe groove which is already described. In addition, a length of thegroove formed in each of the first and second main surfaces of the firstvibrational portion of each of the vibrational arms 20, 31 is alsowithin a range of 0.45 mm to 1.25 mm in the same manner as the width ofthe groove which is already described.

Moreover, it is quite obvious that the part widths W₁ and W₃ alreadydescribed are defined as follows. Namely, W₁ represents a distance inthe width direction of the groove measured from a first outer edge ofthe groove to a first outer edge of the corresponding one of thevibrational arms 20, 31 and W₃ represents a distance in the widthdirection of the groove measured from a second outer edge opposite thefirst outer edge of the groove to a second outer edge opposite the firstouter edge of the corresponding one of the vibrational arms 20, 31, andeach of the distance W₁ and the distance W₃ is less than 0.015 mm,preferably, within a range of 0.003 mm to 0.012 mm in the same way asthe width of the groove which is already described.

Also, the groove formed in each of the first and second main surfaces ofthe first vibrational portion of each of the vibrational arms 20, 31 hasa first outer edge and a second outer edge not opposite the first outeredge in the width direction, and a first distance in the width directionof the groove measured from the first outer edge of the groove to afirst outer edge of the corresponding one of the vibrational arms 20, 31is different from or equal to a second distance in the width directionof the groove measured from the second outer edge of the groove to asecond outer edge of the corresponding one of the vibrational arms 20,31.

In addition, the second vibrational portion of each of the vibrationalarms 20, 31 has third and fourth opposite main surfaces, and a metalfilm for adjusting an oscillation frequency of the quartz crystal tuningfork resonator is disposed on at least one of the third and fourthopposite main surfaces of the second vibrational portion of each of thevibrational arms 20, 31. Moreover, the second vibrational portion ofeach of the vibrational arms 20, 31 may have a generally tapered shapeor a substantially constant width along the length of the correspondenceone of the vibrational arms 20, 31, namely, not variable width. In otherwords, the second vibrational portion of each of the vibrational arms20, 31 comprises a plurality of portions having a first portionincluding a first width and a second portion including a second widthgreater than or substantially equal to the first width. In addition, alength of the first vibrational portion of each of the vibrational arms20, 31 is greater than or equal to a length of the second vibrationalportion of the corresponding one of the vibrational arms 20, 31.

Also, the width W₆ is less than 0.45 mm, preferably, within a range of0.045 mm to 0.2 mm, more preferably, within a range of 0.08 mm to 0.4mm, In addition, the width W₆ is greater than the width W of thevibrational arms 20, 31, and the width W₆ is, preferably, within a rangeof 1.1 times of the width W to 3.8 times of the width W to get thequartz crystal tuning fork resonator with the enough resistance againsta shock. and the length L₃ is less than 2.1 mm, preferably, within arange of 0.3 mm to 1.85 mm, more preferably, within a range of 0.3 mm to1.6 mm to reduce a leakage energy by vibration, and also, the widthW_(S) is less than 0.41 mm, preferably, within a range of 0.015 mm to0.14 mm, and the length L₂ is greater than 0.025 mm and less than 0.55mm, preferably, within a range of 0.04 mm to 0.5 mm to get a shock proofquartz crystal resonator having a reduced leakage energy by vibration.In addition, the length L₂ is less than the width W₆ to get the shockproof quartz crystal resonator having the reduced leakage energy byvibration.

Moreover, the distance W₄ and the width W₂ are constructed so thatW₄≧W₂, and more, the distance W₄ is within a range of 0.045 mm to 0.65mm and the width W₂ is within a range of 0.02 mm to 0.12 mm, preferably,within a range of 0.02 mm to 0.04 mm, more preferably, within a range of0.02 mm to 0.035 mm because it is easy to form a very small-sizedresonator shape and grooves formed at the vibrational arms separately bya photo-lithographic process and an etching process, consequently, afrequency stability for a fundamental mode of vibration of the resonatorgets higher than that for a second overtone mode of vibration thereof.In this embodiment, a quartz wafer having a thickness t of 0.045 mm to0.35 mm is used.

For example, in order to get a smaller-sized quartz crystal tuning forkresonator, capable of vibrating in a flexural mode, it is necessary thatthe width W₂ of the groove is less than 0.07 mm, preferably, greaterthan 0.01 mm and less than 0.05 mm, more preferably, within a range of0.025 mm to 0.049 mm and the arm width W is less than 0.18 mm, andpreferably, the W is greater than 0.05 mm and less than 0.1 mm. Also,the thickness t₁ of the groove is within a range of 0.01 mm to 0.085 mmapproximately, and the part widths W₁ and W₃ are less than 0.021 mm,respectively, preferably, less than 0.015 mm and greater than 2×10⁻⁴ mmor within a range of 2×10⁻⁴ to 5×10⁻⁴, more preferably, greater than5×10⁻⁴ mm and less than 3×10⁻³ mm or within a range of 0.003 mm to 0.012mm. As a result, the small-sized quartz crystal tuning fork resonator isobtained with a small capacitance ratio r₁ and a small series resistanceR₁ of a fundamental mode of vibration because even when miniaturized thequartz crystal resonator has very large electromechanical transformationefficiency. In addition, a groove provided on at least one of an obverseface and a reverse face of the vibrational arms of this embodiment maybe a through hole, namely, the thickness of the hole t₁=0.

In more detail, to obtain a quartz crystal tuning fork resonator,capable of vibrating in a flexural mode, and having a frequency of highstability which achieves high time accuracy, it is necessary to obtainthe resonator whose resonance frequency is not influenced by shuntcapacitance because quartz crystal is a piezoelectric material and thestability for frequency is very dependent on the shunt capacitance. Inorder to decrease the influence on the resonance frequency by the shuntcapacitance, a merit value M_(i) plays an important role. Namely, themerit value M_(i) that expresses inductive characteristics, anelectromechanical transformation efficiency and a quality factor of aquartz crystal tuning fork resonator, is defined by a ratio Q_(i)/r_(i)of a quality factor Q_(i) and capacitance ratio r_(i), namely, M_(i) isgiven by M_(i)=Q_(i)/r_(i), where i shows a vibration order of theresonator, and for example, when i=1 and 2, merit values M₁ and M₂ arefor a fundamental mode of vibration of the resonator and a secondovertone mode of vibration thereof, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the merit value M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the stability for frequency of the quartzcrystal tuning fork resonator becomes because the resonance frequencyf_(r) of the resonator is almost never dependent on the shuntcapacitance. Namely, the quartz crystal tuning fork resonator can beprovided with a high time accuracy.

In detail, the quartz crystal tuning fork resonator can be obtained withthe merit value M₁ of the fundamental mode of vibration greater than themerit value M₂ of the second overtone mode of vibration by providing theabove-described tuning fork shape, grooves and dimensions. That is tosay, a relationship of M₁>M₂ is obtained. As an example, when aresonance frequency of a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode is about 32.768 kHz for a fundamental modeof vibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 andl₁/l=0.48, though there is a distribution in production, the resonatorhas a merit value of M₁>65 for the fundamental mode of vibration and amerit value of M₂<30 for the second overtone mode of vibration,respectively. Preferably, the merit value M₂ is less than 15, morepreferably less than 10.

Namely, the quartz crystal tuning fork resonator can be provided withhigh inductive characteristics, good electromechanical transformationefficiency (small capacitance ratio r₁ and small series resistance R₁)and a high quality factor. As a result, a stability for frequency of thefundamental mode of vibration becomes higher than that of the secondovertone mode of vibration, and simultaneously, the second overtone modeof vibration can be suppressed because capacitance ratio r₂ and seriesresistance R₂ of the second overtone mode of vibration become greaterthan capacitance ratio r_(t) and series resistance R₁ of the fundamentalmode of vibration, respectively. In particular, r₂ has a value greaterthan 1500 in this embodiment. In order to ensure the suppression of thesecond overtone mode of vibration, r₂ is, preferably, greater than 1800,more preferably, greater than 2000.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thefrequency of high stability. Consequently, a quartz crystal oscillatorcomprising the quartz crystal tuning fork resonator of this embodimentoutputs an oscillation frequency of the fundamental mode vibration as anoutput signal, and the frequency of the output signal has a very highstability, namely, excellent time accuracy. In other words, the quartzcrystal oscillator of this embodiment has a remarkable effect such thata frequency change by ageing becomes extremely small. Also, anoscillation frequency of the quartz crystal resonator of this embodimentis adjusted so that a frequency deviation is within a range of −100 PPMto +100 PPM to a nominal frequency, e.g. 32.768 kHz, after mounting iton a mounting portion of a case for housing the resonator.

In addition, the groove thickness t₁, shown in FIG. 3, of the presentinvention is the thinnest thickness of the grooves because quartzcrystal is an anisotropic material and the groove thickness t₁ has adistribution when it is formed by a chemical etching method. In detail,a groove shape of the sectional view of vibrational arms in FIG. 3 has arectangular shape, but the groove shape has an about U shape or anarbitrary shape actually. In the above-described embodiments, though thegrooves are constructed at the arms, this invention is not limited tothis, namely, a relationship of the merit values M₁ and M₂ can beapplied to the conventional quartz crystal tuning fork resonator and arelationship of a quartz crystal oscillating circuit comprising anamplification circuit and a feedback circuit can be also applied to theconventional quartz crystal tuning fork resonator to suppress a secondovertone mode vibration and to get a high frequency stability for afundamental mode of vibration of the quartz crystal tuning forkresonator. In addition, the length L₃ of each of the mounting arms 36,37 is greater than the length L₁ of the base portion 40 and less thanthe overall length L_(t) (=L+L₁) of the quartz crystal resonator 10, asis apparent from FIG. 2.

FIG. 3 shows an A-A′ cross-sectional view of the vibrational arms 20 and31 of the quartz crystal resonator 10 in FIG. 2, and electrodeconstruction within the grooves. The vibrational arm 20 has grooves 21and 22 cut into it, which include a portion of central linear line ofthe arm 20. The grooves 21 and 22 have a first set of electrodes 23 and24 of the same electrical polarity, while the side surfaces of the arm20 have a second set of electrodes 25 and 26 having an oppositeelectrical polarity to the first set of electrodes 23 and 24. Thevibrational arm 31 has grooves 27 and 28 constructed in a similar manneras the vibrational arm 20. The grooves 27 and 28 have a third set ofelectrodes 29 and 30 of the same electrical polarity, and the sidesurfaces of the vibrational arm 31 have a fourth set of electrodes 32and 33 with the opposite electrical polarity to the third electrodes 29and 30. The electrodes disposed on the vibrational arms 20 and 31 areconnected as shown in FIG. 3, namely, two electrode terminals ofdifferent electrical polarity C-C′ are obtained.

In detail, the first set of electrodes 23 and 24 disposed on the grooves21 and 22 of the vibrational arm 20 have the same electrical polarity asthe fourth set of electrodes 32 and 33 disposed on both side surfaces ofthe vibrational arm 31, while the second set of electrodes 25 and 26disposed on both side surfaces of the vibrational arm 20 have the sameelectrical polarity as the third set of electrodes 29 and 30 disposed onthe grooves 27 and 28 of the arm 31. When a direct voltage is appliedbetween the electrode terminals C-C′, an electric field Ex occurs alongthe arrow direction inside the vibrational arms 20 and 31. As theelectric field Ex occurs perpendicular to the electrodes disposed on thevibrational arms, as shown in the arrow signs, the electric field Ex hasa very large value and a large distortion occurs at the vibrationalarms. As a result, a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode is obtained with a small series resistanceR₁ and a high quality factor Q because even when miniaturized there is avery large electromechanical transformation efficiency for theresonator.

FIG. 4 shows an A-A′ cross-sectional view of another embodiment of thevibrational arms 20 and 31 of the quartz crystal resonator 10 in FIG. 2.The vibrational arm 20 has a through groove 21 a, which include aportion of central linear line of the arm 20. The through groove 21 ahas a first set of electrodes 23 a and 24 a of the same electricalpolarity, while the side surfaces of the arm 20 have a second set ofelectrodes 25 and 26 having an opposite electrical polarity to the firstset of electrodes 23 a and 24 a. The vibrational arm 31 has a throughgroove 27 a constructed in a similar manner as the vibrational arm 20.The through groove 27 a has a third set of electrodes 29 a and 30 a ofthe same electrical polarity, and the side surfaces of the vibrationalarm 31 have a fourth set of electrodes 32 and 33 with the oppositeelectrical polarity to the third electrodes 29 a and 30 a. Theelectrodes disposed on the vibrational arms 20 and 31 are connected asshown in FIG. 4, namely, two electrode terminals of different electricalpolarity E-E′ are obtained.

In detail, the first set of electrodes 23 a and 24 a disposed on thethrough groove 21 a of the vibrational arm 20 have the same electricalpolarity as the fourth set of electrodes 32 and 33 disposed on both sidesurfaces of the vibrational arm 31, while the second set of electrodes25 and 26 disposed on both side surfaces of the vibrational arm 20 havethe same electrical polarity as the third set of electrodes 29 a and 30a disposed on the through groove 27 a of the arm 31. When a directvoltage is applied between the electrode terminals E-E′, an electricfield Ex occurs along the arrow direction inside the vibrational arms 20and 31. As the electric field Ex occurs perpendicular to the electrodesdisposed on the vibrational arms, as shown in the arrow signs, theelectric field Ex has a very large value and a large distortion occursat the vibrational arms. As a result, a quartz crystal tuning forkresonator capable of vibrating in a flexural mode is obtained with asmall series resistance R₁ and a high quality factor Q because even whenminiaturized there is a very large electromechanical transformationefficiency for the resonator.

FIG. 5 shows a plan view of a quartz crystal resonator 50 of a secondembodiment of the present invention, and which is a quartz crystaltuning fork resonator capable of vibrating in a flexural mode. Theresonator 50 comprises vibrational arms 60 and 71 and a base portion 80attached to the vibrational arms, and the base portion 80 has a mountingarm 77 protruding from the base portion, and the mounting arm 77 ismounted on a mounting portion of a package comprising a case for housingthe resonator and a lid for covering an open end of the case. Inaddition, each of the vibrational arms 60 and 71 has a first mainsurface and a second main surface and side surfaces, and the vibrationalarms 60 and 71 have grooves 61 and 67, respectively, each of which hasstepped portions comprising a first stepped portion and a second steppedportion. Also, the resonator 50 has the same cutting angles θ_(y), θ_(x)and θ_(z) and the same dimensions W₁, W₂, W₃, W₄, W₅, W, L₁, L₂, L₃, L₄and L as the resonator of FIG. 2.

In more detail, the groove 61 is constructed to include a portion of acentral linear line 81 of the arm 60, and the groove 67 is similarlyconstructed to include a portion of a central linear line 82 of the arm71. Each of the grooves 61 and 67 has a width W₂, and the width W₂includes a portion of the central linear lines 81 and 82 because a largemoment of inertia occurs at the arms 60 and 71. In this embodiment, theresonator is a quartz crystal tuning fork resonator capable of vibratingin a flexural mode and which can vibrate in a fundamental mode of aninverse phase easily. As a result, the quartz crystal tuning forkresonator capable of vibrating in a fundamental mode of an inverse phasecan be obtained with a small series resistance R₁ and a high qualityfactor Q₁.

In addition, electrodes 65 and 66 are disposed on side surfaces of thevibrational arm 60 and electrode 63 is disposed on a surface of thegroove 61, and which is connected to electrodes 72 and 73 disposed onside surfaces of the vibration arm 71. Also, the electrode 63 isconnected to an electrode disposed on a surface of the mounting arm 77through an electrode disposed on a surface of a connecting portion 75.Similar to this, an electrode 69 is disposed on a surface of the groove67, which extends on a surface of the mounting arm 77 having a firstmounting arm portion including a first width W₆ and a second mountingarm portion including a second width greater than the first width W₆,and the connecting portion 75. Also, the electrode 69 is connected tothe electrodes 65 and 66 and is connected to an electrode disposed on asurface of each of the first and second mounting arm portions of themounting arm 77 through a electrode disposed on a surface of theconnecting portion 75.

FIG. 6 shows a plan view of a quartz crystal resonator 90 of a thirdembodiment of the present invention, which is a quartz crystal tuningfork resonator capable of vibrating in a flexural mode. The resonator 90comprises vibrational arms 91 and 92 and a base portion 95 attached tothe vibrational arms, and the base portion 90 has a mounting arm 96protruding from the base portion. In this embodiment, the mounting arm96 is between the vibrational arms 91 and 92 and is mounted on amounting portion of a package comprising a case for housing theresonator and a lid for covering an open end of the case. In addition,each of the vibrational arms 91 and 92 has a first main surface and asecond main surface opposite the first main surface and side surfaces,and the vibrational arms 91 and 92 have grooves 93 and 94, respectively,each of which has stepped portions comprising a first stepped portionand a second stepped portion. Also, the resonator 90 has the samecutting angles θ_(y), θ_(x) and θ_(z) as the quartz crystal resonator 10of FIG. 2. In this embodiment, the quartz crystal tuning fork resonatorcan vibrate in a flexural mode of a fundamental mode of an inversephase.

In detail, similar to the resonator of FIG. 2, the groove 93 is alsoconstructed to include a portion of a central linear line of the arm 91,and also, the groove 94 is similarly constructed to include a portion ofa central linear line of the arm 92. Each of the grooves 93 and 94 has awidth W₂, and the width W₂ includes a portion of the central linearlines because a large moment of inertia occurs at the vibrational arms91 and 92 and which can vibrate in a flexural mode easily. As a result,the quartz crystal tuning fork resonator capable of vibrating in afundamental mode can be obtained with a small series resistance R₁ and ahigh quality factor Q₁.

In addition, the base portion 95 has a length L₁ and a width W_(H).Also, each of the vibrational arms 91 and 92 has a width W, part widthsW₁ and W₃ and a width W₂ of the groove, namely, there is a relationshipof W=W₁+W₂+W₃. In detail, the resonator 90 has the same dimensions L₁,W_(H), W₁, W₂, W₃, and W and the same relationship as the resonator 10of FIG. 2. Moreover, the mounting arm 96 has a width W₁₁ and there is aspaced-apart distance W₁₀ between the vibrational arm 91 or thevibrational arm 92 and the mounting arm 96. In order to get a quartzcrystal tuning fork resonator with reduced leakage energy by vibrationof the vibrational arms, the distance W₁₀ is within a range of 0.032 mmto 0.21 mm and the width W₁₁ is within a range of 0.12 mm to 0.21 mm orwithin a range of 0.21 mm to 0.88 mm. In addition, to get a shockproofquartz crystal tuning fork resonator, W₁₁ has a relationship of (1.2 to7.6)×W. In this embodiment, a total width W_(t)(=2W+2W₁₀+W₁₁) is lessthan 1.3 mm, preferably, within a range of 0.4 mm to 1.2 mm, morepreferably, within a range of 0.52 mm to 1.2 mm, to get a miniaturequartz crystal tuning fork resonator.

FIG. 7 shows a B-B′ cross-sectional view of the vibrational arms 91 and92 of the resonator 90 in FIG. 6. The vibrational arm 91 has grooves 93and 97 cut into it, and the grooves 93 and 97 have a first set ofelectrodes 100 and 101 of the same electrical polarity, while the sidesurfaces of the arm 91 have a second set of electrodes 99 and 102 havingan opposite electrical polarity to the first set of electrodes 100 and101. The vibrational arm 92 has grooves 94 and 98 constructed in asimilar manner as the vibrational arm 91. The grooves 94 and 98 have athird set of electrodes 106 and 107 of the same electrical polarity, andthe side surfaces of the vibrational arm 92 have a fourth set ofelectrodes 105 and 108 with the opposite electrical polarity to thethird electrodes 106 and 107. The electrodes disposed on the vibrationalarms 91 and 92 are connected as shown in FIG. 7, namely, two electrodeterminals of different electrical polarity D-D′ are obtained.

In detail, the first set of electrodes 100 and 101 disposed on thegrooves 93 and 97 of the vibrational arm 91 have the same electricalpolarity as the fourth set of electrodes 105 and 108 disposed on bothside surfaces of the vibrational arm 92 and an electrode 104 disposed onthe mounting arm 96, while the second set of electrodes 99 and 102disposed on both side surfaces of the vibrational arm 91 have the sameelectrical polarity as the third set of electrodes 106 and 107 disposedon the grooves 94 and 98 of the arm 92 and an electrode 103 disposed onthe mounting arm 96. When a direct voltage is applied between theelectrode terminals D-D′, an electric field Ex occurs along the arrowdirection inside the vibrational arms 91 and 92. As the electric fieldEx occurs perpendicular to the electrodes disposed on the vibrationalarms, as shown in the arrow signs, the electric field Ex has a verylarge value and a large distortion occurs at the vibrational arms.Consequently, a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode is obtained with a small series resistanceR₁ and a high quality factor Q because even when miniaturized, there isvery large electromechanical transformation efficiency for theresonator.

FIG. 8 shows a plan view of a quartz crystal resonator 110 of a fourthembodiment of the present invention, which is a quartz crystal tuningfork resonator. The resonator 110 comprises vibrational arms 111 and 112and a base portion 113 attached to the vibrational arms, and the baseportion 113 has mounting arms 114 and 115 protruding from the baseportion, each of which is mounted on a mounting portion of a packagecomprising a case for housing the resonator and a lid for covering anopen end of the case. In this embodiment, the vibrational arms 111 and112 have grooves 116 and 117, respectively. In more detail, each of thevibrational arms 111 and 112 has an end portion connected to the baseportion and a free end portion, when a distance measured from the endportion to the free end portion is a length L, each of the vibrationalarms has a width W between the end portion and half a length L/2 of eachof the vibrational arms and a width W_(e) between half the length L/2and the length L of the free end portion of each of the vibrationalarms, and the width W is less than the width W_(e). In this embodiment,the quartz crystal tuning fork resonator can vibrate in a flexural modeand vibrate in a fundamental mode of an inverse phase.

Similar to this, a quartz crystal tuning fork resonator 120 of a fifthembodiment of the present invention is shown in FIG. 9 showing a planview thereof. The resonator 120 comprises vibrational arms 121 and 122and a base portion 123 attached to the vibrational arms, and the baseportion 123 has a mounting arm 124 protruding from the base portion. Inthis embodiment, the mounting arm 124 is between the vibrational arms121 and 122 and the vibrational arms 121 and 122 have grooves 125 and126, respectively. For this case the width W is also less than the widthW_(e) similar to that of FIG. 8.

FIG. 10 shows a plan view of a quartz crystal resonator 130 of a sixthembodiment of the present invention, which is a quartz crystal tuningfork resonator. The resonator 130 comprises vibrational arms 131 and 132and a base portion 133 attached to the vibrational arms, and the baseportion 133 has mounting arms 134 and 135 protruding from the baseportion, each of which is mounted on a mounting portion of a packagecomprising a case for housing the resonator and a lid for covering anopen end of the case. In this embodiment, the vibrational arms 131 and132 have grooves 136 and 137, respectively.

In more detail, each of the vibrational arms 131 and 132 has an endportion connected to the base portion and a free end portion, when adistance measured from the end portion to the free end portion is alength L, each of the vibrational arms has a width W located between theend portion and half a length L/2 of each of the vibrational arms and awidth W_(e) located between half the length L/2 and the length L of thefree end portion of each of the vibrational arms, and the width W isless than the width W_(e). In addition, a ratio of (W_(e)/W) is within arange of 1.2 to 4.2, preferably, within a range of 1.3 to 3.8, morepreferably, within a range of 1.6 to 3.5. As already-described, thewidth W is less than 0.18 mm, and preferably, the W is greater than 0.05mm and less than 0.1 mm. It is needless to say that this relationship isapplicable to all i.e. each of quartz crystal tuning fork resonators ofthis invention including a quartz crystal tuning fork resonator whichwill be described in FIG. 11. In this embodiment, the quartz crystaltuning fork resonator can vibrate in a flexural mode and vibrate in afundamental mode of an inverse phase.

As above-described, each of the vibrational arms has the width W and thewidth W_(e) greater than the width W in this embodiment, but, thisinvention is not limited to this, namely, each of the vibrational armsmay comprise a plurality of different thicknesses having a firstthickness T and a second thickness T_(e) greater than the firstthickness T. In other words, each of the vibrational arms comprises afirst vibrational portion having the first thickness T and a secondvibrational portion having the second thickness T_(e) greater than thefirst thickness T. Namely, the width W is replaced with the thickness Tand the width W_(e) is replaced with the thickness T_(e). This inventionmay include the relationships of the thickness T_(e) greater than thethickness T and the width W_(e) greater than the width W. As is shown inFIG. 10, at least one groove is formed in each of upper and lower facesof the first vibrational portion of each of the vibrating arms.

In addition, the second vibrational portion having the width W_(e)and/or the thickness T_(e) has opposite main surfaces and opposite sidesurfaces, e.g. the opposite main surfaces has a third main surface and afourth main surface and the opposite side surfaces has a third sidesurface and a fourth side surface, and e.g. a plurality of metal filmscomprising a first metal film having a first thickness and a secondmetal film having a second thickness greater than the first thicknessare disposed on at least one or each of the third and fourth mainsurfaces of the second vibrational portion of each of the vibrationalarms, and the first thickness of the first metal film is less than ahalf of the second thickness of the second metal film, preferably, onethird of the second thickness of the second metal film.

Also, at least one of the first and second metal films disposed on atleast one of the third and fourth main surfaces of the secondvibrational portion of each of the vibrational arms extends on at leastone or each of the third and fourth side surfaces of the secondvibrational portion of the corresponding one of the vibrational arms andat least one of the first and second metal films comprises gold orsilver.

For another instance, the second vibrational portion of each of thevibrational arms has a third main surface and a fourth main surfaceopposite the third main surface and each of the third and fourth mainsurfaces has a first main portion and a second main portion. Inaddition, a first metal film is disposed on each of the first and secondmain portions of at least one of the third and fourth main surfaces ofthe second vibrational portion of each of the vibrational arms and asecond metal film is disposed on the first metal film disposed on eachof the first and second main portions of the at least one of the thirdand fourth main surfaces of the second vibrational portion of each ofthe vibrational arms.

Also, a thickness of the second metal film on the first metal filmdisposed on the second main portion of the at least one of the third andfourth main surfaces of the second vibrational portion of each of thevibrational arms is greater than a thickness of the second metal film onthe first metal film disposed on the first main portion of the at leastone of the third and fourth main surfaces of the second vibrationalportion of the corresponding one of the vibrational arms, and the secondmetal film is disposed on the first metal film disposed on the secondmain portion of the at least one of the third and fourth main surfacesof the second vibrational portion of each of the vibrational arms sothat the quartz crystal tuning fork resonator has an oscillationfrequency lower than 32.75 kHz.

In addition, a thickness of the first metal film disposed on the firstmain portion of the at least one of the third and fourth main surfacesof the second vibrational portion of each of the vibrational arms issubstantially equal to a thickness of the first metal film disposed onthe second main portion of the at least one of the third and fourth mainsurfaces of the second vibrational portion of the corresponding one ofthe vibrational arms and the first metal film comprises chromium ornickel.

For further instance, the second vibrational portion of each of thevibrational arms has a third side surface and a fourth side surfaceopposite the third side surface, and a fifth side surface free invibration. The third side surface is connected to the fourth sidesurface through the fifth side surface, and a third electrode isdisposed on the third side surface, a fourth electrode is disposed onthe fourth side surface and a fifth electrode is disposed on the fifthside surface, the third electrode disposed on the third side surface isconnected to the fourth electrode disposed on the fourth side surfacethrough the fifth electrode disposed on the fifth side surface toprevent the resonator from chipping end portions of the vibrational armsthereof when shocked.

Similar to this, a quartz crystal tuning fork resonator 140 of a seventhembodiment of the present invention is shown in FIG. 11 showing a planview thereof. The resonator 140 comprises vibrational arms 141 and 142and a base portion 143 attached to the vibrational arms, and the baseportion 143 has a mounting arm 144 protruding from the base portion. Inthis embodiment, the mounting arm 144 protrudes from the base portion143 having a length within a range of 0.03 mm to 0.36 mm, preferably,within a range of 0.03 mm to 0.3 mm, and is formed between thevibrational arms 141 and 142 so that the mounting arm 144 extends in acommon direction with the vibrational arms 141, 142 and a length of themounting arm 144 is within a range of 0.3 mm to 1.85 mm, preferably,within a range of 0.3 mm to 1.6 mm, and the vibrational arms 141 and 142have grooves 145, 146, respectively. For this case the width W is alsoless than the width W_(e) similar to the resonator of FIG. 10.

In other words, each of the vibrational arms 141, 142 comprises a firstvibrational portion having a first width W and a second vibrationalportion having a second width W_(e) greater than the first width W, asis shown in FIG. 11. Also, the groove 145 is formed in at least one oreach of upper and lower faces of the first vibrational portion of thevibrational arm 141 and the groove 146 is formed in at least one or eachof upper and lower faces of the first vibrational portion of thevibrational arm 142. In addition, a length of the second vibrationalportion of each of the vibrational arms 141, 142 is less than orsubstantially equal to a length of the first vibrational portion of thecorresponding one of the vibrational arms 141, 142 and is within a rangeof 0.2 mm to 0.45 mm, preferably, within a range of 0.2 mm to 0.38 mm.

In addition, a width of the second vibrational portion of each of thevibrational arms 141, 142 is greater than or substantially equal to thelength of the base portion 143 to get the quartz crystal tuning forkresonator miniaturized.

Moreover, the mounting arm 144 comprises a plurality of arm portionshaving a first arm portion including a first width W_(m1) and a secondarm portion including a second width W_(m2) greater than the first widthW_(m1), and at least one of the first width W_(m1) of the first armportion of the mounting arm 144 and the second width W_(m2) of thesecond arm portion of the mounting arm 144 is greater than orsubstantially equal to the length of the base portion 143. Also, a ratioof (W_(m2)/W_(m1)) is within a range of 1.5 to 4.6, preferably, within arange of 2.4 to 4.3.

In addition, the first width W_(m1) of the first arm portion of themounting arm 144 is different from the second width W_(e) of the secondvibrational portion of each of the vibrational arms 141, 142. In orderto get the quartz crystal tuning fork resonator which is strong againsta shock, the first width W_(m1) of the first arm portion of the mountingarm 144 is greater than or substantially equal to the second width W_(e)of the second vibrational portion of each of the vibrational arms 141,142 and is, preferably, within a range of 0.12 mm to 0.37 mm.

In this embodiment shown in FIG. 11, the length of the mounting arm 144is less than a length of each of the vibrational arms 141, 142, but thelength of the mounting arm may be greater than or substantially equal tothe length of each of the vibrational arms 141, 142 and is within arange of 0.5 mm to 1.6 mm.

In addition, a first spaced-apart distance between the first arm portionof the mounting arm 144 and the second vibrational portion of thevibrational arm 141 is defined by W₁₀, similar to this, a secondspaced-apart distance between the first arm portion of the mounting arm144 and the second vibrational portion of the vibrational arm 142 isalso defined by W₁₀, Also, the first arm portion of the mounting arm 144has a width W₁₁, and when an overall width W_(o) is defined by(2W_(e)+2W₁₀+W₁₁), the overall width W_(o) is within a range of 0.045 mmto 0.08 mm, preferably, within a range of 0.045 mm to 0.062 mm.

Moreover, at least three grooves having first, second and third groovesare formed in each of the upper and lower faces of the first vibrationalportion of each of the vibrational arms 141, 142 so that each of thefirst, second and third grooves is formed in the width direction of eachof the vibrational arms 141, 142 and has a width within a range of 0.005mm to 0.035 mm, preferably, within a range of 0.007 mm to 0.02 mm. Also,at least one of the first, second and third grooves is formed in acentral linear portion of each of the upper and lower faces of the firstvibrational portion of each of the vibrational arms 141, 142.

As a first example, a case has first and second mounting portions, andthe first arm portion of the mounting arm 144 is mounted on the firstmounting portion of the case and the second arm portion of the mountingarm 144 is mounted on the second mounting portion of the case. Inaddition, a first electrode is disposed on a surface of the grooveformed in the at least one or each of the upper and lower faces of thefirst vibrational portion of each of the vibrational arms 141, 142 and asecond electrode is disposed on a surface of each of the first andsecond arm portions of the mounting arm 144 so that the first electrodedisposed on the surface of the groove formed in the at least one or eachof the upper and lower faces of the first vibrational portion of one ofthe vibrational arms 141, 142 is connected to the second electrodedisposed on the surface of the first arm portion of the mounting arm 144and the first electrode disposed on the surface of the groove formed inthe at least one or each of the upper and lower faces of the firstvibrational portion of the other of the vibrational arms 141, 142 isconnected to the second electrode disposed on the surface of the secondarm portion of the mounting arm 144.

Moreover, a third electrode is disposed on a surface of each of thefirst and second mounting portions of the case, and the third electrodedisposed on the surface of the first mounting portion of the case isconnected to the second electrode disposed on the surface of the firstarm portion of the mounting arm 144 and the third electrode disposed onthe surface of the second mounting portion of the case is connected tothe second electrode disposed on the surface of the second arm portionof the mounting arm 144. In addition, the third electrode disposed onthe surface of the first mounting portion of the case has an electricalpolarity opposite to an electrical polarity of the third electrodedisposed on the surface of the second mounting portion of the case.

As a second example, a case has first and second mounting portions andthe second arm portion of the mounting arm 144 has a first portion and asecond portion, and the first portion of the second arm portion of themounting arm 144 is mounted on the first mounting portion of the caseand the second portion of the second arm portion of the mounting arm 144is mounted on the second mounting portion of the case.

In addition, a first electrode is disposed on a surface of the grooveformed in the at least one or each of the upper and lower faces of thefirst vibrational portion of each of the vibrational arms 141, 142 and asecond electrode is disposed on a surface of each of the first andsecond portions of the second arm portion of the mounting arm 144 sothat the first electrode disposed on the surface of the groove formed inthe at least one or each of the upper and lower faces of the firstvibrational portion of one of the vibrational arms 141, 142 is connectedto the second electrode disposed on the surface of the first portion ofthe second arm portion of the mounting arm 144 and the first electrodedisposed on the surface of the groove formed in the at least one or eachof the upper and lower faces of the first vibrational portion of theother of the vibrational arms 141, 142 is connected to the secondelectrode disposed on the surface of the second portion of the secondarm portion of the mounting arm 144.

Moreover, a third electrode is disposed on a surface of each of thefirst and second mounting portions of the case, and the third electrodedisposed on the surface of the first mounting portion of the case isconnected to the second electrode disposed on the surface of the firstportion of the second arm portion of the mounting arm 144 and the thirdelectrode disposed on the surface of the second mounting portion of thecase is connected to the second electrode disposed on the surface of thesecond portion of the second arm portion of the mounting arm 144. Inaddition, the third electrode disposed on the surface of the firstmounting portion of the case has an electrical polarity opposite to anelectrical polarity of the third electrode disposed on the surface ofthe second mounting portion of the case.

Especially, the quartz crystal tuning fork resonator of the fourthembodiment to the seventh embodiment can be miniaturized with a smallseries resistance R₁ and a high quality factor Q₁ because it has a widthW_(e) greater than a width W, and the width W_(e) operates as a mass.

Next, a value of a piezoelectric constant e′₁₂ is described, which is ofgreat importance and necessary to excite a quartz crystal tuning forkresonator capable of vibrating in a flexural mode of the presentinvention. The larger a value of the piezoelectric constant e′₁₂becomes, the higher electromechanical transformation efficiency becomes.The piezoelectric constant e′₁₂ of the present invention can be definedby a function of the cutting angles θ_(y), θ_(x) and θ_(z) shown in FIG.1, and piezoelectric constants e₁₁=0.171 C/m² and e₁₄=−0.0406 C/m² ofquartz crystal. In order to obtain a quartz crystal tuning forkresonator, capable of vibrating in a flexural mode and having a smallseries resistance R₁ and a high quality factor Q, the piezoelectricconstant e′₁₂ of the present invention is within a range of 0.1 C/m² to0.19 C/m² in the absolute value. It is, therefore, easily understoodthat this value is enough large to obtain the quartz crystal tuning forkresonator with a small series resistance R₁ and a high quality factor Q.

Especially, in order to obtain a quartz crystal tuning fork resonatorcapable of vibrating in a flexural mode with a much smaller seriesresistance R₁, the piezoelectric constant e′₁₂ is preferably within arange of 0.12 C/m² to 0.19 C/m² in the absolute value.

In addition, as an example, a quartz crystal tuning fork resonatorcomprises a plurality of vibrational arms having a first vibrational armand a second vibrational arm, and a groove having a first steppedportion and a second stepped portion is formed in at least one of afirst main surface and a second main surface of each of the first andsecond vibrational arms, in which a first electrode is disposed on thefirst stepped portion of the groove, a second electrode is disposed onthe second stepped portion of the groove, and a third electrode isdisposed on each of side surfaces of each of the first and secondvibrational arms, in which the piezoelectric constant e′₁₂(=e′_(12i)) isbetween the first electrode and the third electrode disposed opposite tothe first electrode, and the piezoelectric constant e′₁₂(=e′_(12o)) isbetween the second electrode and the third electrode disposed oppositeto the second electrode, and in which the piezoelectric constantse′_(12i) and e′_(12o) are within the range of 0.12 C/m² to 0.19 C/m² inthe absolute value, respectively, and a product of the e′_(12i) and thee′_(12o) is greater than 0.

As an another example, a quartz crystal tuning fork resonator comprisesa plurality of vibrational arms having a first vibrational arm and asecond vibrational arm, and a through hole having a first side surfaceand a second side surface is formed in each of the first and secondvibrational arms, in which a first electrode is disposed on the firstside surface of the through hole, a second electrode is disposed on thesecond side surface of the through hole, and a third electrode isdisposed on each of side surfaces of each of the first and secondvibrational arms, in which the piezoelectric constant e′₁₂(=e′_(12i)) isbetween the first electrode and the third electrode disposed opposite tothe first electrode, and the piezoelectric constant e′₁₂(=e′_(12o)) isbetween the second electrode and the third electrode disposed oppositeto the second electrode, and in which the piezoelectric constantse_(12i) and e_(12o) are within the range of 0.12 C/m² to 0.19 C/m² inthe absolute value, respectively, and a product of the e′_(12i) and thee′_(12o) is greater than 0.

Therefore, the quartz crystal tuning fork resonator described above hasa small series resistance R₁ and a high quality factor Q, and also afrequency of high stability.

FIG. 12 shows a plan view of a width-extensional mode quartz crystalresonator 150 constructing an electronic apparatus of the presentinvention, and which vibrates in a width-extensional mode. Thewidth-extensional mode resonator 150 comprises a vibrational portion151, connecting portions 152, 152 a and supporting portions 153 and 154connected to a mounting portion 155 constructing the supportingportions. Namely, the vibrational portion 151 is connected to thesupporting portions 153, 154 having the mounting portion 155 through theconnecting portions 152, 152 a. In addition, an electrode 151 a isdisposed on an obverse surface of the vibrational portion 151 and anelectrode 151 b (not visible) is disposed on a reverse surface of thevibrational portion 151.

In more detail, the electrode 151 a disposed on the obverse surface ofthe vibrational portion 151 is connected to an electrode 153 a disposedon the mounting portion 155, while the electrode 151 b disposed on thereverse surface of the vibrational portion 151 is connected to anelectrode 154 a disposed on the mounting portion 155 through anelectrode 154 b disposed on a side surface of the mounting portion.Namely, a pair of electrodes is disposed on the obverse and reversesurfaces of the vibrational portion 151. Also, the vibrational portion151 has a width W₀ and a length L₀. In general, a ratio W₀/L₀ is lessthan 0.35. In addition, the mounting portion 155 is mounted on amounting portion of a package comprising a case for housing theresonator and a lid for covering an open end of the case. In thisembodiment, a cutting angle of the resonator is within a range of ZYlwt(80° to 100°)/(−10° to +10°)/(75° to +115°) and a piezoelectric constante′₃₁ of the resonator is within a range of 0.1 C/m² to 0.19 C/m² in theabsolute value to obtain the resonator with a small series resistance R₁and a high quality factor Q.

Similar to this, a length-extensional mode quartz crystal resonator canbe obtained by replacing the width W₀ with the length L₀. In this casethe connecting portions are formed in the width direction. In thisembodiment, a cutting angle of the length-extensional mode resonator iswithin a range of ZYlwt (80° to 100°)/(−10° to +10°)/(−35° to +35°) anda piezoelectric constant e′₃₂ of the resonator is within a range of 0.12C/m² to 0.19 C/m² in the absolute value to obtain the resonator with asmall series resistance R₁ and a high quality factor Q.

FIG. 13( a) and FIG. 13( b) show a plan view of a thickness shear modequartz crystal resonator 156 constructing an electronic apparatus of thepresent invention and a F-F′ sectional view of the thickness shear moderesonator 156 capable of vibrating in a thickness shear mode. Theresonator 156 comprises a vibrational portion 157 having a width W₀, alength L₀ and a thickness T₀, and electrodes 158 and 159 are disposed onan obverse surface and a reverse surface so that the electrodes haveopposite electrical polarity each other. Namely, a pair of electrodes isdisposed on the vibrational portion 157. Also, the resonator 156 ishoused in a package comprising a case for housing the resonator and alid for covering an open end of the case. In this embodiment, a cuttingangle of the resonator is within a range of ZYlwt (−5° to +5°)/±(37° to58°)/(85° to 95°) and a piezoelectric constant e′₃₄ of the resonator iswithin a range of 0.055 C/m² to 0.14 C/m² in the absolute value toobtain the resonator with a small series resistance R₁ and a highquality factor Q. In order to obtain much smaller series resistance R₁,the piezoelectric constant e′₃₄ of the resonator is preferably within arange of 0.085 C/m² to 0.12 C/m² in the absolute value.

FIG. 14 shows a plan view of a Lame mode quartz crystal resonator 210constructing an electronic apparatus of the present invention, andvibrating in a Lame mode. The Lame mode resonator 210 comprises avibrational portion 211, connecting portions 212, 213 and supportingportions 214, 215 having mounting portions 216 and 217. Namely, thevibrational portion 211 is connected to the supporting portions 214, 215through the connecting portions 212, 213. In addition, an electrode 218is disposed on an obverse surface of the vibrational portion 211 and anelectrode 219 (not visible) is disposed on a reverse surface of thevibrational portion 211.

In more detail, the electrode 218 disposed on the obverse surface of thevibrational portion 211 is extended into the mounting portion 217, whilethe electrode 219 disposed on the reverse face of the vibrationalportion 211 is extended into the mounting portion 216. Namely, a pair ofelectrodes is disposed on the obverse and reverse surfaces of thevibrational portion 151. Also, the vibrational portion 211 has a widthW₀ and a length L₀. In general, a ratio L₀/W₀ is approximately equal tom for a fundamental mode of vibration and an overtone mode of vibrationof the resonator, where m is an order of vibration of the resonator andan integer. For example, when a Lame mode quartz crystal resonator hasone of m=1, 2, 3 and n, the resonator vibrates in a fundamental mode form=1, a second overtone mode for m=2, a third overtone mode for m=3 andan n^(th) overtone mode for m=n.

Also, the m has a close relationship to the number of electrodesdisposed on the vibrational portion. For example, when an electrode isdisposed opposite each other on both of an obverse surface and a reversesurface of the vibrational portion, this is called “the number of twoelectrodes”, in other words, “a pair of electrodes”. Namely, thevibrational portion has the number of p electrodes, where p is an evennumber such as 2, 4, 6, 8 and 10. As an example, when p of thevibrational portion comprises 6, the vibrational portion vibrates in athird overtone mode. In this example, three pairs of electrodes aredisposed on the vibrational portion. Namely, the third overtone mode ofvibration is a principal vibration. As is apparent from thisrelationship, there is a relationship of m=p/2.

Therefore, the principal vibration vibrates in the order of vibrationcorresponding to the number of an electrode pair or electrode pairs. Forexample, the principal vibration vibrates in a fundamental mode ofvibration, a second overtone mode of vibration and a third overtone modeof vibration, respectively, for an electrode pair, two electrode pairsand three electrode pair disposed on the vibrational portion. In detail,when m_(e) electrode pairs are disposed on the vibrational portion, theprincipal vibration vibrates in an n^(th) overtone mode of vibration,and m_(e) corresponds to the n, where m_(e) is an integer. It isneedless to say that this concept can be applied to a width-extensionalmode quartz crystal resonator and a length-extensional mode quartzcrystal resonator.

In more detail, an even number of electrodes are disposed on the obverseand reverse surfaces of the vibrational portion and the electrodesdisposed opposite each other has an opposite electrical polarity. Inaddition, each of the mounting portions 216, 217 is mounted on amounting portion of a package comprising a case for housing theresonator and a lid for covering an open end of the case. In thisembodiment, a cutting angle of the resonator is within a range of ZYlwt(−5° to +5°)/±(35° to 60°)/±(40° to 50°) and a piezoelectric constante′₃₂ of the resonator is within a range of 0.045 C/m² to 0.13 C/m² inthe absolute value to obtain the resonator with a small seriesresistance R₁ and a high quality factor Q.

FIG. 15( a) and FIG. 15( b) show a plan view of a resonator for sensingangular velocity constructing an electronic apparatus of the presentinvention and a G-G′ sectional view of the resonator. In thisembodiment, the resonator 220 comprises a quartz crystal tuning forkresonator, capable of vibrating in a flexural mode and comprisingvibrational arms 221, 222 and a base portion 223 attached to thevibrational arms, the base portion 223 is mounted on a mounting portionof a package comprising a case for housing the resonator and a lid forcovering an open end of the case. In addition, each of the vibrationalarms 221 and 222 has a first main surface and a second main surfaceopposite the first main surface and side surfaces, and the vibrationalarm 221 has grooves 224, 230, while the vibrational arm 222 has grooves225, 237, each of which has stepped portions comprising a first steppedportion and a second stepped portion. Also, a cutting angle of theresonator is within a range of ZYlwt (−20° to +20°)/(−25° to +25°)/(−18°to +18°) and a piezoelectric constant e′₁₂ of the resonator is within arange of 0.1 C/m² to 0.19 C/m² in the absolute value. The resonator ofthis embodiment can vibrate in a flexural mode of a fundamental mode andan inverse phase.

In more detail, electrodes 226 and 227 which are of the same electricalpolarity are disposed on the side surfaces such that an electrodeterminal H is defined, while an electrode 228 is disposed inside thegroove 224 and an electrode 229 which is of the same electrical polarityto the electrode 228 is disposed inside the groove 230 such that anelectrode terminal H′ of opposite electrical polarity to the electrodeterminal H is defined. Namely, two electrode terminals H-H′ for an inputsignal are constructed. On the other hand, electrodes 231, 232, 233which are of the same electrical polarity are disposed on the sidesurfaces and inside the grooves 225, 237 such that an electrode terminalI is defined, while electrodes 234, 235, 236 which are of the sameelectrical polarity are disposed on the side surfaces and inside thegrooves 225, 237 such that an electrode terminal I′ of oppositeelectrical polarity to the electrode terminal I is defined. Namely, twoelectrode terminals I-I′ for an output signal are constructed. Theresonator of this embodiment is made of quartz crystal, but may be madeof a piezoelectric material such as lithium tantalite, lithium niobateand ceramics.

FIG. 16( a) and FIG. 16( b) show, respectively, a plan view and a J-J′sectional view of a quartz crystal resonator 230 of an eighth embodimentof the present invention, and which is a quartz crystal tuning forkresonator. The resonator 230 comprises vibrational arms 231 and 232 anda base portion 233 attached to the vibrational arms. In addition, eachof the vibrational arms 231 and 232 has a first main surface and asecond main surface opposite the first main surface and side surfaces,and the first and second main surfaces have central linear portions 242,243, respectively.

In other words, each of the first and second main surfaces of thevibrational arm 231 has the central linear portion 242 and each of thefirst and second main surfaces of the vibrational arm 232 has thecentral linear portion 243. The vibrational arm 231 has grooves 234, 236and the vibrational arm 232 has grooves 235, 237. Namely, a plurality ofgrooves having the grooves 234, 236 is formed in at least one or each ofthe first and second main surfaces of the vibrational arms 231 and aplurality of grooves having the grooves 235, 237 is formed in at leastone or each of the first and second main surfaces of the vibrationalarms 232. In addition, each of the grooves 234, 236 is formed betweenthe central linear portion 242 and an outer edge of the vibrational arm231. Similar to this, each of the grooves 235, 237 is formed between thecentral linear portion 243 and an outer edge of the vibrational arm 232.Namely, each of the grooves 234, 236 is formed in the width direction ofthe vibrational arm 231 and each of the grooves 235, 237 is formed inthe width direction of the vibrational arm 232.

Moreover, each of the grooves 234, 235, 236 and 237 has a width W₈, anda width W₇ including a portion of the central linear lines 242 and 243is formed in each of the vibrational arms 231, 232. In detail, a widthW₇ including the central linear portion 242 is formed in at least one oreach of the first and second main surfaces of the vibrational arm 231and a width W₇ including the central linear portion 243 is formed in atleast one or each of the first and second main surfaces of thevibrational arm 232. In more detail, a width W₇ of the vibrational arm231 represents a distance in the width direction of the grooves 234, 236measured from an outer edge of the groove 234 to an outer edge of thegroove 236. Similar to this, a width W₇ of the vibrational arm 232represents a distance in the width direction of the grooves 235, 237measured from an outer edge of the groove 235 to an outer edge of thegroove 237.

In addition, a distance W₉ is formed in the width direction of thevibrational arms 231, 232 between an outer edge of the groove and anouter edge of the corresponding one of the vibrational arms. Namely, W₉of the vibrational arm 231 represents each of a distance in the widthdirection of the groove 234 measured from an outer edge of the groove234 to an outer edge of the vibrational arm 231 and a distance in thewidth direction of the groove 236 measured from an outer edge of thegroove 236 to an outer edge of the vibrational arm 231, while W₉ of thevibrational arm 232 represents each of a distance in the width directionof the groove 235 measured from an outer edge of the groove 235 to anouter edge of the vibrational arm 232 and a distance in the widthdirection of the groove 237 measured from an outer edge of the groove237 to an outer edge of the vibrational arm 232.

In detail, a width W of the arms 231 and 232 has generally arelationship of W=W₇+2W₈+2W₉, and the width W₈ is constructed so thatW₈≧W₇, W₉. In this embodiment, also, the grooves are constructed at thearms so that a ratio W₈/(W/2) of the width W₈ and a half width of thewidth W is greater than 0.35 and less than 1, preferably, within a rangeof 0.35 to 0.95. In addition, the width W₇ is less than 0.05 mm,preferably, less than 0.03 mm and the width W₈ is greater than 0.008 mm,preferably, within a range of 0.009 mm to 0.05 mm, more preferably,within a range of 0.015 mm to 0.05 mm, and the distance W₉ is greaterthan 0.003 mm, preferably, within a range of 0.0035 mm to 0.012 mm, morepreferably, within a range of 0.0045 mm to 0.01 mm to obtain a verylarge moment of inertia of the vibrational arms. That is, the quartzcrystal tuning fork resonator, capable of vibrating in a fundamentalmode, and having a frequency of high stability can be provided with asmall series resistance R₁, a high quality factor Q₁ and a smallcapacitance ratio r₁ because it has a very large electromechanicaltransformation efficiency.

In FIG. 16( b), the vibrational arm 231 has grooves 234, 236, 238 and240 cut into it. The grooves 234, 236, 238 and 240 have a first set ofelectrodes 256, 257, 258 and 259 of the same electrical polarity, whilethe side surfaces of the arm 231 have a second set of electrodes 244,245 having an opposite electrical polarity to the first set ofelectrodes 256, 257, 258 and 259. The vibrational arm 232 has grooves235, 237, 239 and 241 constructed in a similar manner as the vibrationalarm 231. The grooves 235, 237, 239 and 241 have a third set ofelectrodes 252, 253, 254 and 255 of the same electrical polarity, andthe side surfaces of the vibrational arm 232 have a fourth set ofelectrodes 250, 251 with the opposite electrical polarity to the thirdelectrodes 252, 253, 254 and 255. The electrodes disposed on thevibrational arms 231, 232 are connected as shown in FIG. 16( b), namely,two electrode terminals of different electrical polarity K-K′ areobtained.

In detail, the first set of electrodes 256, 257, 258 and 259 disposed onthe grooves 234, 236, 238 and 240 of the vibrational arm 231 have thesame electrical polarity as the fourth set of electrodes 250, 251disposed on both side surfaces of the vibrational arm 232, while thesecond set of electrodes 244, 245 disposed on both side surfaces of thevibrational arm 231 have the same electrical polarity as the third setof electrodes 252, 253, 254 and 255 disposed on the grooves 235, 237,239 and 241 of the arm 232. When a direct current voltage is appliedbetween the electrode terminals K-K′, an electric field Ex occurs alongthe arrow direction inside the vibrational arms 231, 232. As theelectric field Ex occurs perpendicular to the electrodes disposed on thevibrational arms, as shown in the arrow signs, the electric field Ex hasa very large value and a large distortion occurs at the vibrationalarms. As a result, a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode is obtained with a small series resistanceR₁ and a high quality factor Q because even when miniaturized there is avery large electromechanical transformation efficiency for theresonator.

FIG. 17 shows a plan view of a quartz crystal unit of a first embodimentof the present invention and omitting a lid. The quartz crystal unit 160comprises the quartz crystal tuning fork resonator 10 shown in FIG. 2, acase 165 for housing the resonator and a lid for covering an open end ofthe case (not shown here). Also, the resonator 10 has mounting arms 36and 37, each of which is mounted on a mounting portion 166 and amounting portion 167 of the case 165. In detail, an electrode disposedon the mounting arm 36 is connected to an electrode disposed on themounting portion 166 by adhesives 168 or a metal such as solder, andsimilarly, an electrode disposed on the mounting arm 37 is connected toan electrode disposed on the mounting portion 167 by adhesives 169 or ametal.

FIG. 18 shows a plan view of a quartz crystal unit of a secondembodiment of the present invention and omitting a lid. The quartzcrystal unit 170 comprises the quartz crystal tuning fork resonator 50shown in FIG. 5, a case 175 for housing the resonator and a lid forcovering an open end of the case (not shown here). Namely, the resonatorcomprises vibrational arms and a base portion. Also, the case 175 hasmounting portions 176, 177 and the resonator 50 has the mounting arm 77which is mounted on each of the mounting portions 176, 177 and has thefirst mounting arm portion including the first width W₆ (see, FIG. 5)and the second mounting arm portion including the second width greaterthan the first width W₆ and protruding from the base portion. Namely,the second mounting arm portion including the second width is mounted onthe mounting portion 177 of the case 175. In detail, an electrodedisposed on a surface of the second mounting arm portion of the mountingarm 77 is connected to an electrode disposed on a surface of themounting portion 177 by adhesives 179 or a metal such as solder, andsimilarly, an electrode disposed on the base portion of the resonator 50is connected to the electrode 63 disposed on the surface of the groove61 (see, FIG. 5) and an electrode disposed on a surface of the mountingportion 176 by adhesives 178 or a metal such as solder.

FIG. 19 shows a cross-sectional view of a quartz crystal unit of a thirdembodiment of the present invention. The quartz crystal unit 180comprises a contour mode quartz crystal resonator 185 or a thicknessshear mode quartz crystal resonator 185, a case 181 and a lid 182. Inmore detail, the resonator 185 is mounted on a mounting portion 184 ofthe case 181 by conductive adhesives 76 or solder. Also, the case 181and the lid 182 are connected through a connecting member 183. Forexample, the contour mode resonator 185 in this embodiment is the sameresonator as one of the quartz crystal tuning fork resonators 10, 50,90, 110, 120, 130, 140, 220 and 230 described in detail in FIG. 2-FIG.11 and FIG. 15-FIG. 16.

In this embodiment, circuit elements are connected at outside of thequartz crystal unit to get a quartz crystal oscillator. Namely, only thequartz crystal tuning fork resonator is housed in the unit and also, itis housed in the unit in vacuum. In this embodiment, the quartz crystalunit of a surface mounting type is shown, but the quartz crystal tuningfork resonator may be housed in a tubular type, namely, a quartz crystalunit of the tubular type. In addition, the quartz crystal unit of thepresent invention includes any shape of a quartz crystal unit comprisinga quartz crystal resonator, a case and a lid to house the quartz crystalresonator in vacuum.

As an example of any shape of the quartz crystal unit, when the quartzcrystal tuning fork resonator 10 is formed in a quartz crystal wafer, anend portion of the mounting arm 36 is not connected to an end portion ofthe mounting arm 37, as is shown in FIGS. 2 and 17, but the end portionof the mounting arm 36 may be connected to the end portion of themounting arm 36 in the quartz crystal wafer to get a connected (closed)mounting arm. In detail, the connected (closed) mounting arm comprisesone end portion and the other end portion each connected to the baseportion.

Also, each of the connected mounting arm and the base portion has anupper face and a lower face, namely, a first surface and a secondsurface opposite the first surface. For this case, a quartz crystal unitcomprises a case and a lid, and each of the case and the lid has aninterior space and an open end. Also, the lower face (the secondsurface) of each of the connected mounting arm and the base portion ismounted on a mounting portion of the case and the upper face (the firstsurface) of each of the connected mounting arm and the base portion ismounted on a mounting portion of the lid, namely, the lower face (thesecond surface) of each of the connected mounting arm and the baseportion is connected to the open end of the case and the upper face (thefirst surface) of each of the connected mounting arm and the baseportion is connected to the open end of the lid to cover the open end ofeach of the case and the lid. A width of the open end of each of the lidand the case is less, preferably, equal to, more preferably, greaterthan a width of the connected mounting arm and/or the base portion toget a big connected power.

When each of the case and the lid has no through hole, at least one ofthe open end of the case and open end of the lid is connected to thecorresponding one of the upper and lower faces of each of the connectedmounting arm and the base portion so that the quartz crystal tuning forkresonator is maintained in a vacuum, and when one of the case and thelid has a through hole including a first diameter and a second diametergreater than the first diameter, a metal or a glass is disposed into thethrough hole of the second diameter to close the through hole of one ofthe case and the lid in a vacuum after the open end of each of the caseand the lid is connected to the corresponding one of the upper and lowerfaces of each of the connected mounting arm and the base portion.

As above-described, the base portion is located between the open end ofthe case and the open end of the lid, for example, a part having an areaof the base portion is located between the open end of the case and theopen end of the lid. It is needless to say that the quartz crystaltuning fork tines are located between the interior space of the case andthe interior space of the lid. Also, the connection of the open end ofthe case is performed simultaneously with the connection of the open endof the lid, but, according to the present invention, the connection ofthe open end of the case may be performed in a step different from theconnection of the open end of the lid, namely, the connection of theopen end of the case is performed after or before the connection of theopen end of the lid is performed.

Also, a first electrode (metal film) is disposed on each of a surface ofthe open end of the lid and the upper face of each of the connectedmounting arm and the base portion and a second electrode (metal film) isdisposed on each of a surface of the open end of the case and the lowerface of each of the connected mounting arm and the base portion. The lidis connected to the connected mounting arm and the base portion throughthe first electrode disposed on the surface of the open end of the lidand the first electrode disposed on the upper face of each of theconnected mounting arm and the base portion, while the case is connectedto the connected mounting arm and the base portion through the secondelectrode disposed on the surface of the open end of the case and thesecond electrode disposed on the lower face of each of the connectedmounting arm and the base portion.

Namely, each of the connection of the lid and the connected mounting armand the base portion and the connection of the case and the connectedmounting arm and the base portion is performed by an anode connectionmethod. In addition, the first electrode disposed on each of the surfaceof the open end of the lid and the upper face of each of the connectedmounting arm and the base portion has an electrical polarity opposite toan electrical polarity of the second electrode disposed on each of thesurface of the open end of the case and the lower face of each of theconnected mounting arm and the base portion.

Also, the case and the lid are made of a piezoelectric material such asquartz crystal or a glass or ceramics and have a thermal expansioncoefficient less than that of the quartz crystal tuning fork resonator.In addition, the present invention includes the following example,namely, one of the case and the lid comprises a plurality of throughholes having a first through hole and a second through hole and anelectrode is disposed on a surface of each of the first and secondthrough holes.

In addition, one of the case and the lid comprises a first electrode anda second electrode each of which is disposed on an outer surface of theone of the case and the lid. Also, the vibrational arms shown in FIG. 3having two electrode terminals including first and second electrodeterminals are located between an inner surface in the interior space ofthe case and an inner surface in the interior space of the lid, and thefirst electrode terminal of the vibrational arms is connected to thefirst electrode disposed on the outer surface of the one of the case andthe lid through the electrode disposed on the surface of the firstthrough hole and the second electrode terminal of the vibrational armsis connected to the second electrode disposed on the outer surface ofthe one of the case and the lid through the electrode disposed on thesurface of the second through hole.

In this embodiment, one of the case and the lid comprises the first andsecond through holes, but this invention is not limited to this, namely,the lid comprises an outer surface on which a first electrode isdisposed and a first through hole having a surface on which an electrodeis disposed and the case comprises an outer surface on which a secondelectrode is disposed and a second through hole having a surface onwhich an electrode is disposed.

For this case, the first electrode terminal of the vibrational arms isconnected to the first electrode disposed on the outer surface of thelid through the electrode disposed on the surface of the first throughhole of the lid and the second electrode terminal of the vibrationalarms is connected to the second electrode disposed on the outer surfaceof the case through the electrode disposed on the surface of the secondthrough hole of the case. In addition, a metal or a glass is disposedinto each of the first and second through holes to close each of thefirst and second through holes and at least one of the first and secondthrough holes is closed in a vacuum using the metal or the glass.

Also, instead of the quartz crystal tuning fork resonator and thethickness shear mode quartz crystal resonator, one of alength-extensional mode quartz crystal resonator, a width-extensionalmode quartz crystal resonator and a Lame mode quartz crystal resonatorwhich are a contour mode quartz crystal resonator, respectively, or aSAW (Surface Acoustic Wave) resonator or a piezoelectric resonator forsensing angular velocity (angular velocity sensor) made of quartzcrystal or ceramics may be housed in the unit.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 20.

FIG. 20 shows a cross-sectional view of a quartz crystal oscillator of afirst embodiment of the present invention. The quartz crystal oscillator190 comprises a quartz crystal oscillating circuit, a case 191 and a lid192.

In this embodiment, circuit elements constructing the oscillatingcircuit are housed in a quartz crystal unit comprising a contour modequartz crystal resonator 195 or a thickness shear mode quartz crystalresonator 195, the case 191 and the lid 192. Also, the oscillatingcircuit of this embodiment comprises an amplifier 197 including afeedback resistor, the resonator 195, a plurality of capacitors (notshown here) and a drain resistor (not shown here), and a CMOS inverteris used as the amplifier 197.

In addition, in this embodiment, the resonator 195 is mounted on amounting portion 194 of the case 191 by conductive adhesives 196 orsolder. As described above, the amplifier 197 is housed in the quartzcrystal unit and mounted on the case 191. Also, the case 191 and the lid192 are connected through a connecting member 193.

FIG. 21 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator of the presentinvention. The quartz crystal oscillating circuit 201 comprises anamplifier (CMOS inverter) 202, a feedback resistor 204, a drain resistor207, a plurality of capacitors 205, 206 and a quartz crystal resonator203. Namely, the oscillating circuit 201 comprises an amplificationcircuit 208 having the amplifier 202 and the feedback resistor 204, anda feedback circuit 209 having the drain resistor 207, the capacitors205, 206 and the quartz crystal resonator 203. The quartz crystalresonator 203 is one of the resonators already described above. Forexample, when the resonator 203 is a quartz crystal tuning forkresonator capable of vibrating in a flexural mode, an output signal ofthe oscillating circuit 201 is outputted through a buffer circuit (notshown in FIG. 21), and is an oscillating frequency of a fundamental modeof vibration of the resonator.

In other words, the oscillation frequency of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is outputted fromthe oscillating circuit through the buffer circuit as an output signal.According to the present invention, a nominal frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator is within a range of 10 kHz to 200 kHz. Especially, afrequency of 32.768 kHz is very available for use in an electronicapparatus of the present invention. In general, the output signal has anoscillation frequency which is within a range of −100 PPM to +100 PPM tothe nominal frequency, e.g. 32.768 kHz.

In more detail, the quartz crystal oscillator in this example comprisesa quartz crystal oscillating circuit and a buffer circuit, namely, thequartz crystal oscillating circuit comprises an amplification circuitand a feedback circuit, and the amplification circuit comprises anamplifier (CMOS inverter) and a feedback resistor and the feedbackcircuit comprises a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode, a drain resistor and a plurality ofcapacitors. Also, the quartz crystal tuning fork resonator alreadydescribed in FIG. 2-FIG. 11 and FIG. 15-FIG. 16 is used in a quartzcrystal oscillator of the present invention. Instead of the quartzcrystal tuning fork resonator, an another contour mode quartz crystalresonator such as a length-extensional mode quartz crystal resonator, awidth-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator or a thickness shear mode quartz crystal resonator ora resonator for sensing angular velocity may be used.

FIG. 22 shows a diagram of the feedback circuit of FIG. 21. In thisembodiment, the feedback circuit has a quartz crystal tuning forkresonator capable of vibrating in a flexural mode. Now, when angularfrequency of the quartz crystal tuning fork resonator 203, a resistancevalue Rd of the drain resistor 207, capacitance values C_(g), C_(d) ofthe capacitors 205, 206, crystal impedance R_(ei) of the quartz crystalresonator 203, an input voltage V₁, and an output voltage V₂ are taken,a feedback rate β_(i) is defined by β_(i)=|V₂|_(i)/|V₁|_(i), where ishows a vibration order, for example, when i=1 and 2, β₁ and β₂ are afeedback rate for a fundamental mode of vibration and a second overtonemode of vibration of the resonator, respectively.

In addition, load capacitance C_(L) is given by C_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) and R_(d)>>R_(ei), thefeedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²), where k isexpressed by a function of ω_(i), R_(d) and R_(ei). Also, R_(ei) isapproximately equal to series resistance R_(i) of the resonator.

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of a resonancefrequency for the fundamental mode of vibration and the overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when C_(L) has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why maximum amplitude of theovertone mode of vibration becomes smaller than that of the fundamentalmode of vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

As it is also one object of the present invention to provide a quartzcrystal oscillator having a flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having afrequency of high stability (high time accuracy) of an output signal,and having reduced electric current consumption, load capacitance C_(L)is less than 25 pF in this embodiment to reduce electric currentconsumption. To get much reduced electric current consumption, C_(L) ispreferably less than 15 pF because the electric current consumption isproportional to C_(L). More preferably, C_(L) is greater than 2 pF andless than 15 pF to satisfy each of the reduced electric currentconsumption and a phase condition of a second overtone mode of vibrationof the resonator insufficient in an oscillation circuit of theoscillator.

In addition, in order to suppress the second overtone mode of vibrationof the resonator and to obtain the quartz crystal oscillator having anoutput signal of an oscillation frequency of a fundamental mode ofvibration of the resonator, the quartz crystal oscillator comprising anamplification circuit and a feedback circuit is constructed so that itsatisfies a relationship of α₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are,respectively, an amplification rate of the fundamental mode of vibrationand the second overtone mode of vibration of the amplification circuit,and β₁ and β₂ are, respectively, a feedback rate of the fundamental modeof vibration and the second overtone mode of vibration of the feedbackcircuit.

In other words, the quartz crystal oscillator is constructed so that aratio of the amplification rate α₁ of the fundamental mode of vibrationand the amplification rate α₂ of the second overtone mode of vibrationof the amplification circuit is greater than that of the feedback rateβ₂ of the second overtone mode of vibration and the feedback rate β₁ ofthe fundamental mode vibration of the feedback circuit, and also aproduct of the amplification rate α_(l) and the feedback rate β₁ of thefundamental mode of vibration is greater than 1. A description of afrequency of high stability in the quartz crystal oscillator will beperformed later.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode of vibration of theresonator and when i=2, negative resistance −RL₂ is for a secondovertone mode of vibration of the resonator. In this embodiment, thequartz crystal oscillating circuit is constructed so that a ratio of anabsolute value of negative resistance −RL₁ of the fundamental mode ofvibration of the amplification circuit and series resistance R₁ of thefundamental mode of vibration is greater than that of an absolute valueof negative resistance −RL₂ of the second overtone mode of vibration ofthe amplification circuit and series resistance R₂ of the secondovertone mode of vibration.

That is, the oscillating circuit is constructed so that it satisfies arelationship of |−RL₁/R₁>|−RL₂|/R₂. By constructing the oscillatingcircuit like this, an oscillation of the second overtone mode can besuppressed, as a result of which a frequency of oscillation of thefundamental mode of vibration can be output as an output signal becausethe oscillation of the fundamental mode generates easily in theoscillating circuit. In more detail, an absolute value of the negativeresistance −RL₁ is greater than 55 kΩ and less than 800 kΩ, preferably,within a range of 60 kΩ to 500 kΩ, more preferably, within a range of 60kΩ to 285 kΩ, and an absolute value of the negative resistance −RL₂ isless than 200 kΩ, preferably, less than 105 kΩ, more preferably, lessthan 80 kΩ to suppress the frequency of oscillation of the secondovertone mode of the quartz crystal tuning fork resonator in theoscillating circuit and to obtain the frequency of oscillation of thefundamental mode thereof.

In this embodiment, a quartz crystal tuning fork resonator is used, but,instead of the tuning fork resonator, an another contour mode quartzcrystal resonator such as a width-extensional mode quartz crystalresonator, a length-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator may be used in a quartz crystal oscillatorof the present invention. In this case, a principal vibration of thecontour mode quartz crystal resonator is outputted from an oscillatingcircuit constructing the quartz crystal oscillator through a buffercircuit. In order to suppress a sub-vibration of the contour mode quartzcrystal resonator, the quartz crystal oscillator comprising anamplification circuit and a feedback circuit is constructed so that itsatisfies a relationship of α_(p)/α_(s)>β_(s)/β_(p) and α_(p)β_(p)>1,where α_(p) and α_(s) are, respectively, an amplification rate of theprincipal vibration and the sub-vibration of the amplification circuit,and β_(p) and β_(s) are, respectively, a feedback rate of the principalvibration and the sub-vibration of the feedback circuit.

Similar to the quartz crystal tuning fork resonator, for the contourmode quartz crystal resonator, a quartz crystal oscillating circuit ofthe present invention is constructed so that a ratio of an absolutevalue of negative resistance −RL_(p) of the principal vibration of theamplification circuit and a series resistance R_(p) of the principalvibration is greater than that of an absolute value of negativeresistance −RL_(s) of the sub-vibration of the amplification circuit anda series resistance R_(s) of the sub-vibration. That is, the oscillatingcircuit is constructed so that it satisfies a relationship of|−RL_(p)|/R_(p)>|−RL_(s)|/R_(s). By constructing the oscillating circuitlike this, an oscillation of the sub-vibration can be suppressed, as aresult of which a frequency of oscillation of the principal vibrationcan be outputted as an output signal because the oscillation of theprincipal vibration generates easily in the oscillating circuit. Inaddition, the principal vibration and the sub-vibration have the samemode of vibration and a different order of vibration each other.

FIG. 23 shows a block diagram of an embodiment of an electronicapparatus of the present invention, and illustrating the diagram of afacsimile apparatus. As shown in FIG. 23, the apparatus generallycomprises a modem, a phonetic circuit, a timepiece circuit, a printingportion, a taking portion, an operation portion and a display portion.In this principle, perception and scanning of reflection light of lightprojected on manuscript in the taking portion are performed by CCD(Charge Coupled Device), in addition, light and shade of the reflectionlight are transformed into a digital signal, and the signal is modulatedby the modem and is sent to a phone line(communication line). Also, in areceiving side, a received signal is demodulated by the modem and isprinted on a paper in the print portion by synchronizing the receivedsignal with a signal of a sending side. In addition, the display portioncomprises at least one of a liquid crystal display (LCD) portion, aplasma display panel (PDP) portion, a surface-conductionelectron-emitter display (SED) portion and an organicelectroluminescence display (OED) portion.

In FIG. 23, a quartz crystal resonator is used as a CPU clock of thecontrol portion and the printing portion, as a clock of the phoneticcircuit and the modem, and as a time standard of the timepiece. Namely,the resonator constructs a quartz crystal oscillator and an outputsignal of the oscillator is used. Like this, a plurality of oscillatorsis used for the electronic apparatus. For example, it is used as asignal to display time at the display portion. In this case, a quartzcrystal tuning fork resonator, capable of vibrating in a flexural modeis generally used, and e.g. as the CPU clock, a contour mode quartzcrystal resonator such as a length-extensional mode quartz crystalresonator, a width-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator or a thickness shear mode quartz crystalresonator is used. To get the facsimile apparatus of this embodimentwhich operates normally, an accuracy signal of output of the oscillatoris required for the facsimile apparatus, which is one of the electronicapparatus of the present invention. Also, a digital display and ananalogue display are included in the display of the present invention.

In this embodiment, though the facsimile apparatus is shown as anexample of an electronic apparatus of the present invention, the presentinvention is not limited to this, namely, the present invention includesall electronic apparatus, each of which comprises a quartz crystaloscillator and a display portion at least, for example, cellar phones,telephones, a TV set, cameras, a video set, video cameras, pagers,personal computers, printers, CD players, MD players, electronic musicalinstruments, car navigators, car electronics, timepieces, IC cards andso forth. In addition, the electronic apparatus may have an anotheroscillator comprising a piezoelectric resonator for sensing angularvelocity made of quartz crystal, ceramics, lithium tantalite and lithiumniobate. Also, the electronic apparatus of the present invention maycomprise a battery (cell), e.g. a lithium battery or a fuel cell whichis housed in the electronic apparatus of the present invention.

Thus, the electronic apparatus of the present invention comprising adisplay portion and a quartz crystal oscillator at least may operatenormally because the quartz crystal oscillator comprises the quartzcrystal oscillating circuit with a frequency of high stability, namely,a frequency of high reliability.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode of vibration and a second overtonemode of vibration in the electrical equivalent circuit of the resonator.In addition, the resonator has a quality factor Q₁ for the fundamentalmode of vibration and a quality factor Q₂ for the second overtone modeof vibration. Also, the motional capacitance C₁ of the fundamental modeof vibration of the resonator is greater than the motional capacitanceC₂ of the second overtone mode of vibration thereof from therelationship of r₁ less than r₂ shown in the already-describedparagraph.

In addition, a ratio (L_(1m)/L_(2m)) of a motional inductance L_(1m) ofthe fundamental mode of vibration of the resonator and a motionalinductance L_(2m) of the second overtone mode of vibration thereof isless than 42 approximately from the relationships of r₁ less than r₂ andω₂=6.5ω₁ approximately, where ω₁ and ω₂ represent an angular frequencyof the fundamental mode of vibration and the second overtone mode ofvibration, respectively, of the resonator. Also the ratio(L_(1m)/L_(2m)) is less than 6.5(Q₁/Q₂) from the relationship of R₁<R₂.As a result, an output signal having an oscillation frequency of thefundamental mode of vibration of the resonator is output in anoscillating circuit through a buffer circuit because a phase conditionof the fundamental mode of vibration is much better than that of thesecond overtone mode of vibration in the oscillating circuit.

In detail, the tuning fork resonator of this embodiment is provided sothat the influence on resonance frequency of the fundamental mode ofvibration by the shunt capacitance becomes smaller than that of thesecond overtone mode of vibration by the shunt capacitance, namely, sothat it satisfies a relationship of S₁=r₁/2Q₁ ²<S₂=r₂/2Q₂ ², preferably,S₁<S₂/2, where S₁ and S₂ are called “a stable factor of frequency” ofthe fundamental mode of vibration and the second overtone mode ofvibration. As a result, the tuning fork resonator, capable of vibratingin the fundamental mode and having a frequency of high stability can beprovided because the influence on the resonance frequency of thefundamental mode of vibration by the shunt capacitance C₀ is asextremely small as it can be ignored. In this embodiment S₂ has a valuegreater than 0.13×10⁻⁶ to suppress the second overtone mode of vibrationof the resonator.

Though the detailed description is performed concerning each of theembodiments of the first embodiment to the eighth embodiment of thepresent invention, the present invention is not limited to theembodiments above-described, but includes a quartz crystal resonatorwhich comprises a quartz crystal tuning fork resonator having a quartzcrystal tuning fork base, and first and second quartz crystal tuningfork arms connected to the quartz crystal tuning fork base, Namely,

As a first example of the quartz crystal tuning fork resonator, each ofthe first and second quartz crystal tuning fork arms comprises aplurality of vibrational portions having a first vibrational portionincluding a first width W_(p1) and a first length L_(p1), a secondvibrational portion including a second width W_(p2) greater than thefirst width W_(p1) and a second length L_(p2) less than or equal to thefirst length L_(p1), and a third vibrational portion including a thirdwidth W_(p3) greater than the second width W_(p2) and a third lengthL_(p3) less than the first length L_(p1) and/or greater than or equal toor less than the second length L_(p2). In other words, there is arelationship of W_(p1)<W_(p2)<W_(p3) and L_(p3)<L_(p1)≧L_(p2) and/orL_(p3)≧L_(p2) or L_(p3)<L_(p2).

In detail, the second vibrational portion is formed between the firstand third vibrational portions and the first vibration is formed in thequartz crystal tuning fork base side than the third vibrational portion.Also, at least one groove is formed in each of upper and lower faces(i.e. a first main surface and a second main surface opposite the firstmain surface) of each or at least one of the first and secondvibrational portions of each of the first and second quartz crystaltuning fork arms. Such a dimension as e.g., a width, a length, partwidths W₁ and W₃ and so on of the at least one groove, an overall lengthof the quartz crystal tuning fork resonator, a width and a length of atleast one mounting arm connected to the quartz crystal tuning fork baseand so forth is determined in the same way as the embodiments alreadydescribed.

As a second example of the quartz crystal tuning fork resonator, aprotruding portion having a length within a range of 0.025 mm to 0.2 mmprotrudes from the quartz crystal tuning fork base and is formed betweenthe first and second quartz crystal tuning fork arms so that theprotruding portion extends in a common direction with the first andsecond quartz crystal tuning fork arms, and also, a first spaced-apartdistance between the protruding portion and the first quartz crystaltuning fork arm is different from i.e. greater than or equal to a secondspaced-apart distance between the protruding portion and the secondquartz crystal tuning fork arm.

In more detail, a first side surface of the protruding portion isopposite a second side surface in the width direction, and an electrodeis disposed on the first and second side surfaces of the protrudingportion so that the electrode disposed on the first side surface of theprotruding portion has an electrical polarity opposite to an electricalpolarity of the electrode disposed on the second side surface of theprotruding portion. Also, the first spaced-apart distance is within arange of 0.04 mm to 0.18 mm and the second spaced-apart distance iswithin a range of 0.03 mm to 0.15 mm. As a result of which, it ispossible to prevent a shirt-circuit which is caused between theelectrodes.

As a third example of the quartz crystal tuning fork resonator, each ofthe first and second quartz crystal tuning fork arms comprises aplurality of vibrational portions having first, second and thirdvibrational portions, the second vibrational portion is formed betweenthe first and third vibrational portions, and each of the first, secondand third vibrational portions of each of the first and second quartzcrystal tuning fork arms has an upper face (a first main surface) and alower face (a second main surface) opposite the upper face (the firstmain surface) each of which has a central linear portion, and first andsecond portions each not including the central linear portion locatedbetween the first and second portions, i.e. has the first and secondportions and the central linear portion in the width direction.

In addition, a groove is formed in the central linear portion of each ofthe upper and lower faces of each of the first and third vibrationalportions of each of the first and second quartz crystal tuning forkarms, and formed in each or at least one of the first and secondportions of each of the upper and lower faces of the second vibrationalportion of each of the first and second quartz crystal tuning fork arms,i.e. not formed in the central linear portion of each of the upper andlower faces of the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms so that the groove of the firstvibrational portion is connected to the groove of the third vibrationalportion through the groove of the second vibrational portion, i.e. sothat the groove of the first vibrational portion is directly connectedto the groove of the second vibrational portion and the groove of thesecond vibrational portion is directly connected to the groove of thethird vibrational portion.

In detail, the groove formed in the central linear portion of each ofthe upper and lower faces of the first vibrational portion of each ofthe first and second quartz crystal tuning fork arms is connected to thegroove formed in the central linear portion of the corresponding one ofthe upper and lower faces of the third vibrational portion of thecorresponding one of the first and second quartz crystal tuning forkarms through the groove formed in each or the at least one of the firstand second portions of the corresponding one of the upper and lowerfaces of the second vibrational portion of the corresponding one of thefirst and second quartz crystal tuning fork arms.

In other words, each of the groove formed in the central linear portionof each of the upper and lower faces of the first vibrational portion ofeach of the first and second quartz crystal tuning fork arms and thegroove formed in the central linear portion of the corresponding one ofthe upper and lower faces of the third vibrational portion of thecorresponding one of the first and second quartz crystal tuning forkarms is directly connected to the groove formed in each or the at leastone of the first and second portions of the corresponding one of theupper and lower faces of the second vibrational portion of thecorresponding one of the first and second quartz crystal tuning forkarms.

In more detail, when a quartz crystal wafer has a first surface and asecond surface opposite the first surface, it is needless to say thatthe upper face of each of the first, second and third vibrationalportions of each of the first and second quartz crystal tuning fork armsis formed at the first surface of the quartz crystal wafer and the lowerface of each of the first, second and third vibrational portions of eachof the first and second quartz crystal tuning fork arms is formed at thesecond surface thereof. Like this, the upper faces are formed at thesame surface which is the first surface of the quartz crystal wafer andthe lower faces are also formed at the same surface which is the secondsurface of the quartz crystal wafer.

For example, the groove formed in the central linear portion of theupper face of the first vibrational portion of each of the first andsecond quartz crystal tuning fork arms is connected to the groove formedin the central linear portion of the upper face of the third vibrationalportion of the corresponding one of the first and second quartz crystaltuning fork arms through the groove formed in each or the at least oneof the first and second portions of the upper face of the secondvibrational portion of the corresponding one of the first and secondquartz crystal tuning fork arms.

In other words, each of the groove formed in the central linear portionof the upper face of the first vibrational portion of each of the firstand second quartz crystal tuning fork arms and the groove formed in thecentral linear portion of the upper face of the third vibrationalportion of the corresponding one of the first and second quartz crystaltuning fork arms is directly connected to the groove formed in each orthe at least one of the first and second portions of the upper face ofthe second vibrational portion of the corresponding one of the first andsecond quartz crystal tuning fork arms.

Similar to this, each of the groove formed in the central linear portionof the lower face of the first vibrational portion of each of the firstand second quartz crystal tuning fork arms and the groove formed in thecentral linear portion of the lower face of the third vibrationalportion of the corresponding one of the first and second quartz crystaltuning fork arms is directly connected to the groove formed in each orthe at least one of the first and second portions of the lower face ofthe second vibrational portion of the corresponding one of the first andsecond quartz crystal tuning fork arms.

As a fourth example of the quartz crystal tuning fork resonator, each ofthe first and second quartz crystal tuning fork arms has an upper faceand a lower face opposite the upper face, and at least one groove isformed in each of the upper and lower faces of each of the first andsecond quartz crystal tuning fork arms. In addition, each of the upperand lower faces of each of the first and second quartz crystal tuningfork arms has a central linear portion, and the at least one grooveformed in each of the upper and lower faces of each of the first andsecond quartz crystal tuning fork arms has a first groove portion formedin the central linear portion, a second groove portion not formed in thecentral linear portion and a third groove portion formed in the centrallinear portion.

Also, the second groove portion is formed between the first and thirdgroove portions in the length direction. Namely, the first grooveportion is connected to the third groove portion through the secondgroove portion, in other words, the second groove portion is directlyconnected to each of the first groove portion and the third grooveportion.

In addition, the second groove portion has a first groove and a secondgroove in the width direction, and the central linear portion of thesecond groove portion is located between the first and second grooves.In more detail, the first groove portion is connected to the thirdgroove portion through each of the first and second grooves of thesecond groove portion, in other words, each of the first and secondgrooves of the second groove portion is directly connected to each ofthe first groove portion and the third groove portion.

Like this, the at least one groove is formed in the central linearportion of each of the upper and lower faces of each of the first andsecond quartz crystal tuning fork arms and is not formed continuously inthe central linear portion along the length of the corresponding one ofthe first and second quartz crystal tuning fork arms, i.e. formeddiscontinuously in the central linear portion along the length of thecorresponding one of the first and second quartz crystal tuning forkarms.

As a fifth example of the quartz crystal tuning fork resonator, each ofthe first and second quartz crystal tuning fork arms has a first mainsurface (an upper face) and a second main surface (a lower face)opposite the first main surface (the upper face) and a first sidesurface and a second side surface opposite the first side surface. Inaddition, each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork arms has a central linearportion, and at least one groove is formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork arms. Also, the at least one grooveformed in the central linear portion of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forkarms has a first surface opposite the first side surface or the secondside surface.

Moreover, when a first distance in the width direction of the at leastone groove measured from a first outer edge of the first surface of theat least one groove to a first outer edge of the first side surface ofthe corresponding one of the first and second quartz crystal tuning forkarms is defined by W₁₁ and a second distance in the width direction ofthe at least one groove measured from a second outer edge of the firstsurface of the at least one groove to a second outer edge of the firstside surface of the corresponding one of the first and second quartzcrystal tuning fork arms is defined by W₁₂, and the first outer edge ofthe first surface of the at least one groove is located in the quartzcrystal tuning fork base side than the second outer edge of the firstsurface of the at least one groove, namely, a location of the firstdistance W₁₁ is in the quartz crystal tuning fork base side than that ofthe second distance W₁₂, there is such a relationship as the firstdistance W₁₁ is greater than the second distance W₁₂, and also each ofthe first distance W₁₁ and the second distance W₁₂ is within a range of0.003 mm to 0.012 mm. Like this, the first distance W₁₁ is differentfrom the second distance W₁₂.

For instance of the first quartz crystal tuning fork arm, in otherwords, the first distance in the width direction of the at least onegroove measured from the first outer edge of the first surface of the atleast one groove to the first outer edge of the first side surface ofthe first quartz crystal tuning fork arm is defined by W₁₁ and thesecond distance in the width direction of the at least one groovemeasured from the second outer edge of the first surface of the at leastone groove to the second outer edge of the first side surface of thefirst quartz crystal tuning fork arm is defined by W₁₂.

Similar to this, for instance of the second quartz crystal tuning forkarm, the first distance in the width direction of the at least onegroove measured from the first outer edge of the first surface of the atleast one groove to the first outer edge of the first side surface ofthe second quartz crystal tuning fork arm is defined by W₁₁ and thesecond distance in the width direction of the at least one groovemeasured from the second outer edge of the first surface of the at leastone groove to the second outer edge of the first side surface of thesecond quartz crystal tuning fork arm is defined by W₁₂.

As is apparent from the above-described contents, the first outer edgeof the first side surface of each of the first and second quartz crystaltuning fork arms is also in the quartz crystal tuning fork base sidethan the second outer edge of the first side surface of thecorresponding one of the first and second quartz crystal tuning forkarms. Also, it is needless to say that a direction of the first distanceW₁₁ is parallel to a direction of the second distance W₁₂ in the widthdirection.

In addition, the first side of the at least one groove formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork arms has a thirdouter edge located between the first and second outer edges of the atleast one groove, and the first side surface of each of the first andsecond quartz crystal tuning fork arms has a third outer edge locatedbetween the first and second outer edges of the corresponding arm. Whena third distance in the width direction of the at least one groovemeasured from the third outer edge of the first surface of the at leastone groove to the third outer edge of the first side surface of thecorresponding one of the first and second quartz crystal tuning forkarms is defined by W₁₃, the third distance W₁₃ is less than the firstdistance W₁₁ and greater than the second distance W₁₂. The thirddistance W₁₃ is also within a range of 0.003 mm to 0.012 mm.

As a result, the quartz crystal tuning fork resonator very small-sizedis obtained with a decreased series resistance R₁ of a fundamental modeof vibration thereof.

As a sixth example of the quartz crystal tuning fork resonator, in orderto get the quartz crystal tuning fork resonator extremely miniaturized,an overall length of the quartz crystal tuning fork resonator is,preferably, less than 1.0 mm, more preferably, within a range of 0.65 mmto 0.98 mm. In addition, a ratio (L_(n1)/L_(b1)) of a length L_(n1) ofeach of the first and second quartz crystal tuning fork arms and alength L_(b1) of the quartz crystal tuning fork base is within a rangeof 2.5 to 9.2, preferably, within a range of 3.6 to 8.8 to get reduceleakage energy by vibration. As a result of which, a quartz crystal unitwhich has a case, the quartz crystal tuning fork resonator mounted on amounting portion of the case and a lid connected to an open end of thecase is obtained with an overall length less than 1.5 mm.

It is, therefore, needless to say that the quartz crystal tuning forkresonator of each of the six examples which has the first example to thesixth example is applied to the quartz crystal tuning fork resonatorsalready described in the embodiments of the first embodiment to theeighth embodiment, and also to each of the quartz crystal unit, thequartz crystal oscillator and the electronic apparatus alreadydescribed.

In addition, as above-described, the present invention includes manyembodiments and examples and each of the embodiments and the examples isdescribed in full detail. However, it is needless to say that thepresent invention is not limited to this, but also includes combinationsof the embodiments and the examples.

As described above, it will be easily understood that the quartz crystalresonator comprising vibrational arms and a base portion, according tothe present invention, may have outstanding effects. Similar to this,the quartz crystal unit and the quartz crystal oscillator, according tothe present invention, may have also outstanding effects. In addition,the electronic apparatus comprising the quartz crystal oscillatorcomprising the quartz crystal oscillating circuit having the quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,and having novel shapes, novel electrode construction and excellentelectrical characteristics, according to the present invention, may havethe outstanding effects. Similar to this, it will be easily understoodthat the electronic apparatus comprising the quartz crystal oscillatorcomprising the quartz crystal oscillating circuit having the anothercontour mode quartz crystal resonator or the thickness shear mode quartzcrystal resonator or the resonator for sensing angular velocity,according to the present invention, may have also the outstandingeffect. In addition to this, while the present invention has been shownand described with reference to preferred embodiments thereof, it willbe understood by those skilled in the art that the changes in shape andelectrode construction can be made therein without departing from thespirit and scope of the present invention.

What is claimed is:
 1. A quartz crystal unit comprising: a quartzcrystal tuning fork resonator having a quartz crystal tuning fork shapeincluding a quartz crystal tuning fork base, and first and second quartzcrystal tuning fork arms connected to the quartz crystal tuning forkbase, each of the first and second quartz crystal tuning fork armshaving a first main surface and a second main surface opposite the firstmain surface; wherein at least one groove is formed in the at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork arms; wherein at least one mounting armhaving a width less than 0.45 mm protrudes from the quartz crystaltuning fork base; and wherein an overall length of the quartz crystaltuning fork resonator is less than 2.1 mm.
 2. A quartz crystal unitaccording to claim 1; wherein the at least one mounting arm has a lengthwithin a range of 0.3 mm to 1.85 mm, a first arm portion including afirst width and a second arm portion including a second width greaterthan the first width, and extends in a common direction with the firstand second quartz crystal tuning fork arms outside the first and secondquartz crystal tuning fork arms; wherein the first arm portion of the atleast one mounting arm is connected to the quartz crystal tuning forkbase through a connecting portion having a length L₂ within a range of0.04 mm to 0.5 mm; wherein a length L₁ of the quartz crystal tuning forkbase is less than 0.5 mm; and further comprising a case having amounting portion and a lid for covering an open end of the case; whereinthe second arm portion of the at least one mounting arm is mounted onthe mounting portion of the case; and wherein the lid is connected tothe case to cover the open end of the case.
 3. A quartz crystal unitaccording to claim 2; wherein the overall length of the quartz crystaltuning fork resonator is within a range of 1.02 mm to 1.95 mm; wherein awidth of the quartz crystal tuning fork base is within a range of 0.15mm to 0.53 mm and the length L_(i) of the quartz crystal tuning forkbase is within a range of 0.015 mm to 0.49 mm; wherein a width of the atleast one groove formed in the at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning fork armsis less than 0.07 mm and a distance in the width direction of the atleast one groove measured from an outer edge of the at least one grooveto an outer edge of the corresponding one of the first and second quartzcrystal tuning fork arms is less than 0.015 mm; wherein a firstelectrode is disposed on a surface of the at least one groove formed inthe at least one of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork arms; wherein a secondelectrode is disposed on a surface of the connecting portion; wherein athird electrode is disposed on a surface of each of the first and secondarm portions of the at least one mounting arm; wherein a fourthelectrode is disposed on a surface of the mounting portion of the case;and wherein the first electrode disposed on the surface of the at leastone groove formed in the at least one of the first and second mainsurfaces of one of the first and second quartz crystal tuning fork armsis connected to the fourth electrode disposed on the surface of themounting portion of the case through the second electrode disposed onthe surface of the connecting portion and the third electrode disposedon the surface of each of the first and second arm portions of the atleast one mounting arm.
 4. A quartz crystal unit according to claim 3;wherein each of the first and second quartz crystal tuning fork armscomprises a plurality of vibrational portions having a first vibrationalportion including a first width and a second vibrational portionincluding a second width greater than the first width, the firstvibrational portion of each of the first and second quartz crystaltuning fork arms having first and second opposite main surfaces; whereinthe at least one groove comprises a groove formed in each of the firstand second opposite main surfaces of the first vibrational portion ofeach of the first and second quartz crystal tuning fork arms so that adistance in the width direction of the groove measured from an outeredge of the groove to an outer edge of the corresponding one of thefirst and second quartz crystal tuning fork arms is within a range of0.003 mm to 0.012 mm; wherein the quartz crystal tuning fork base hastwo cut portions, and a first base portion and a second base portion;wherein the two cut portions are formed between the first and secondbase portions of the quartz crystal tuning fork base, each of the firstand second quartz tuning fork arms being connected to the first baseportion of the quartz crystal tuning fork base; wherein the at least onemounting arm comprises a plurality of mounting arms having first andsecond mounting arms, each of the first and second mounting arms beingconnected to the second base portion of the quartz crystal tuning forkbase and extending in a common direction with the first and secondquartz crystal tuning fork arms outside the first and second quartzcrystal tuning fork arms; wherein the first mounting arm is connected tothe second base portion of the quartz crystal tuning fork base through afirst connecting portion and the second mounting arm is connected to thesecond base portion of the quartz crystal tuning fork base through asecond connecting portion so that the second base portion of the quartzcrystal tuning fork base and the first and second connecting portionshave a U-shape or a concave shape with the first and second mountingarms; wherein the case has first and second mounting portions; andwherein the first mounting arm is mounted on the first mounting portionof the case and the second mounting arm is mounted on the secondmounting portion of the case.
 5. A quartz crystal unit according toclaim 3; wherein each of the first and second quartz crystal tuning forkarms comprises a plurality of vibrational portions having a firstvibrational portion including a generally tapered shape comprised of aplurality of different widths having a first width and a second widthless than the first width, and a second vibrational portion including athird width less than or equal to the first width, the first vibrationalportion of each of the first and second quartz crystal tuning fork armshaving first and second opposite main surfaces each including a centrallinear portion; wherein the at least one groove comprises a grooveformed in the central linear portion of each of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms so that a width of thegroove formed in the central linear portion of each of the first andsecond opposite main surfaces of the first vibrational portion of eachof the first and second quartz crystal tuning fork arms is within arange of 0.025 mm to 0.049 mm, a first distance in the width directionof the groove measured from a first outer edge of the groove to a firstouter edge of the corresponding one of the first and second quartzcrystal tuning fork arms being defined by W₁ and a second distance inthe width direction of the groove measured from a second outer edgeopposite the first outer edge of the groove to a second outer edgeopposite the first outer edge of the corresponding one of the first andsecond quartz crystal tuning fork arms being defined by W₃, and so thateach of the first distance W₁ and the second distance W₃ is within arange of 0.003 mm to 0.012 mm; wherein the second vibrational portion ofeach of the first and second quartz crystal tuning fork arms has thirdand fourth opposite main surfaces; and wherein a metal film foradjusting an oscillation frequency of the quartz crystal tuning forkresonator is disposed on at least one of the third and fourth oppositemain surfaces of the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms.
 6. A quartz crystal unitaccording to claim 3; wherein the quartz crystal tuning fork base hastwo cut portions, and a first base portion and a second base portion;wherein the two cut portions are formed between the first and secondbase portions of the quartz crystal tuning fork base, each of the firstand second quartz crystal tuning fork arms being connected to the firstbase portion of the quartz crystal tuning fork base; wherein the atleast one mounting arm comprises a plurality of mounting arms havingfirst and second mounting arms, each of the first and second mountingarms extending in a common direction with the first and second quartzcrystal tuning fork arms outside the first and second quartz crystaltuning fork arms and having first, second, third, fourth and fifth armportions, each of the first, third and fifth arm portions extendingsubstantially parallel to the first and second quartz crystal tuningfork arms, the first arm portion being connected to the third armportion through the second arm portion extending not parallel to thefirst and second quartz crystal tuning fork arms, and the third armportion being connected to the fifth arm portion through the fourth armportion extending not parallel to the first and second quartz crystaltuning fork arms; wherein the first arm portion of the first mountingarm is connected to the second base portion of the quartz crystal tuningfork base through a first connecting portion and the first arm portionof the second mounting arm is connected to the second base portion ofthe quartz crystal tuning fork base through a second connecting portionso that the second base portion of the quartz crystal tuning fork baseand the first and second connecting portions have a U-shape or a concaveshape with the first arm portions of the first and second mounting arms;wherein the case has first and second mounting portions; and wherein thefifth arm portion of the first mounting arm is mounted on the firstmounting portion of the case and the fifth arm portion of the secondmounting arm is mounted on the second mounting portion of the case.
 7. Aquartz crystal unit according to claim 1; wherein the at least onemounting arm is connected to the quartz crystal tuning fork base havinga length L₁ through a connecting portion having a length L₂; and whereina value of L₁−L₂ is within a range of −0.1 mm to 0.32 mm.
 8. A quartzcrystal unit according to claim 7; wherein the at least one mounting armextends in a common direction with the first and second quartz crystaltuning fork arms outside the first and second quartz crystal tuning forkarms and has a length within a range of 0.3 mm to 1.85 mm; wherein eachof the first and second quartz crystal tuning fork arms comprises aplurality of vibrational portions having a first vibrational portionincluding a first width and a second vibrational portion including asecond width greater than the first width, the first vibrational portionof each of the first and second quartz crystal tuning fork arms havingfirst and second opposite main surfaces; wherein the at least one groovecomprises a groove formed in at least one of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms so that a width of thegroove formed in the at least one of the first and second opposite mainsurfaces of the first vibrational portion of each of the first andsecond quartz crystal tuning fork arms is less than a spaced-apartdistance between the first and second quartz crystal tuning fork armsand less than 0.07 mm, and a distance in the width direction of thegroove measured from an outer edge of the groove to an outer edge of thecorresponding one of the first and second quartz crystal tuning forkarms is less than 0.015 mm; wherein the second vibrational portion ofeach of the first and second quartz crystal tuning fork arms has thirdand fourth opposite main surfaces; and wherein a metal film foradjusting an oscillation frequency of the quartz crystal tuning forkresonator is disposed on at least one of the third and fourth oppositemain surfaces of the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms.
 9. A quartz crystal unitaccording to claim 8; wherein the at least one mounting arm comprisesfirst and second mounting arms, each of the first and second mountingarms protruding from the quartz crystal tuning fork base and extendingin a common direction with the first and second quartz crystal tuningfork arms outside the first and second quartz crystal tuning fork arms;wherein a length of each of the first and second mounting arms is withina range of 0.3 mm to 1.85 mm and a width of each of the first and secondmounting arms is less than 0.45 mm; wherein the first mounting arm isconnected to the quartz crystal tuning fork base through a firstconnecting portion and the second mounting arm is connected to thequartz crystal tuning fork base through a second connecting portion,each of the first and second connecting portions having a width lessthan 0.41 mm; wherein the case has first and second mounting portions;wherein the first mounting arm is mounted on the first mounting portionof the case and the second mounting arm is mounted on the secondmounting portion of the case; wherein each of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms has a central linearportion; wherein the at least one groove comprises a groove formed inthe central linear portion of each of the first and second opposite mainsurfaces of the first vibrational portion of each of the first andsecond quartz crystal tuning fork arms so that a width of the grooveformed in the central linear portion of each of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms is less than thespaced-apart distance between the first and second quartz crystal tuningfork arms and less than 0.07 mm, a first distance in the width directionof the groove measured from a first outer edge of the groove to a firstouter edge of the corresponding one of the first and second quartzcrystal tuning fork arms being defined by W₁ and a second distance inthe width direction of the groove measured from a second outer edgeopposite the first outer edge of the groove to a second outer edgeopposite the first outer edge of the corresponding one of the first andsecond quartz crystal tuning fork arms being defined by W₃, and so thateach of the first distance W₁ and the second distance W₃ is less than0.015 mm.
 10. A quartz crystal unit according to claim 9; wherein thequartz crystal tuning fork base has two cut portions, and a first baseportion and a second base portion; wherein the two cut portions areformed between the first and second base portions of the quartz crystaltuning fork base, each of the first and second quartz crystal tuningfork arms being connected to the first base portion of the quartzcrystal tuning fork base; wherein the first mounting arm is connected tothe second base portion of the quartz crystal tuning fork base throughthe first connecting portion and the second mounting arm is connected tothe second base portion of the quartz crystal tuning fork base throughthe second connecting portion so that the second base portion of thequartz crystal tuning fork base and the first and second connectingportions have a U-shape or a concave shape with the first and secondmounting arms; and wherein a length of the quartz crystal tuning forkbase is less than 0.5 mm.
 11. A quartz crystal unit according to claim9; wherein a first electrode is disposed on a surface of the grooveformed in the central linear portion of each of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms and a second electrodeis disposed on a surface of each of the first and second mountingportions of the case; wherein a third electrode is disposed on a surfaceof each of the first and second connecting portions and a fourthelectrode is disposed on a surface of each of the first and secondmounting arms; wherein the first electrode disposed on the surface ofthe groove formed in the central linear portion of each of the first andsecond opposite main surfaces of the first vibrational portion of one ofthe first and second quartz crystal tuning fork arms is connected to thesecond electrode disposed on the surface of the first mounting portionof the case through the third electrode disposed on the surface of thefirst connecting portion and the fourth electrode disposed on thesurface of the first mounting arm; and wherein the first electrodedisposed on the surface of the groove formed in the central linearportion of each of the first and second opposite main surfaces of thefirst vibrational portion of the other of the first and second quartzcrystal tuning fork arms is connected to the second electrode disposedon the surface of the second mounting portion of the case through thethird electrode disposed on the surface of the second connecting portionand the fourth electrode disposed on the surface of the second mountingarm.
 12. A quartz crystal unit according to claim 1; wherein the atleast one mounting arm has a length L₃ within a range of 0.3 mm to 1.85mm and is connected to the quartz crystal tuning fork base through aconnecting portion having a length L₂ within a range of 0.04 mm to 0.5mm, the at least one mounting arm extending in a common direction withthe first and second quartz crystal tuning fork arms outside the firstand second quartz crystal tuning fork arms; and further comprising acase having a mounting portion and a lid for covering an open end of thecase; wherein the at least one mounting arm is mounted on the mountingportion of the case; wherein the lid is connected to the case to coverthe open end of the case; and wherein a width of the quartz crystaltuning fork base is less than 0.55 mm and a length L₁ of the quartzcrystal tuning fork base is less than 0.5 mm.
 13. A quartz crystal unitaccording to claim 12; wherein the at least one mounting arm comprisesfirst and second mounting arms each having a length L₃ within a range of0.3 mm to 1.85 mm and a width less than 0.45 mm, each of the first andsecond mounting arms protruding from the quartz crystal tuning fork baseand extending in a common direction with the first and second quartzcrystal tuning fork arms outside the first and second quartz crystaltuning fork arms; wherein the first mounting arm is connected to thequartz crystal tuning fork base through a first connecting portion andthe second mounting arm is connected to the quartz crystal tuning forkbase through a second connecting portion, each of the first and secondconnecting portions having a length L₂ within a range of 0.04 mm to 0.5mm and a width less than 0.41 mm; wherein the case has first and secondmounting portions; wherein the first mounting arm is mounted on thefirst mounting portion of the case and the second mounting arm ismounted on the second mounting portion of the case; wherein the quartzcrystal tuning fork resonator has a capacitance ratio r₁ of afundamental mode of vibration and a capacitance ratio r₂ of a secondovertone mode of vibration; wherein an electrode is disposed on asurface of the at least one groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork arms, each of the quartz crystal tuning fork shape,the at least one groove formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork arms and the electrode disposed on the surface of the atleast one groove formed in the at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning fork armshaving a dimension; wherein the dimension of each of the quartz crystaltuning fork shape, the at least one groove formed in the at least one ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork arms and the electrode disposed on thesurface of the at least one groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork arms is determined so that the capacitance ratio r₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof; and wherein the length L₁ of the quartzcrystal tuning fork base is within a range of 0.015 mm to 0.49 mm andthe width of the quartz crystal tuning fork base is within a range of0.15 mm to 0.53 mm.
 14. A quartz crystal unit according to claim 12;wherein each of the first and second quartz crystal tuning fork armscomprises a plurality of vibrational portions having a first vibrationalportion including a first width and a second vibrational portionincluding a second width greater than the first width, the firstvibrational portion of each of the first and second quartz crystaltuning fork arms having first and second opposite main surfaces eachincluding a central linear portion; wherein the at least one groovecomprises a groove formed in the central linear portion of each of thefirst and second opposite main surfaces of the first vibrational portionof each of the first and second quartz crystal tuning fork arms so thata width of the groove formed in the central linear portion of each ofthe first and second opposite main surfaces of the first vibrationalportion of each of the first and second quartz crystal tuning fork armsis less than a spaced-apart distance between the first and second quartzcrystal tuning fork arms and less than 0.07 mm, a first distance in thewidth direction of the groove measured from a first outer edge of thegroove to a first outer edge of the corresponding one of the first andsecond quartz crystal tuning fork arms being defined by W₁ and a seconddistance in the width direction of the groove measured from a secondouter edge opposite the first outer edge of the groove to a second outeredge opposite the first outer edge of the corresponding one of the firstand second quartz crystal tuning fork arms being defined by W₃, and sothat each of the first distance W₁ and the second distance W₃ is lessthan 0.015 mm; wherein the second vibrational portion of each of thefirst and second quartz crystal tuning fork arms has third and fourthopposite main surfaces; and wherein a metal film for adjusting anoscillation frequency of the quartz crystal tuning fork resonator isdisposed on at least one of the third and fourth opposite main surfacesof the second vibrational portion of each of the first and second quartzcrystal tuning fork arms.
 15. A quartz crystal unit according to claim12; wherein each of the first and second quartz crystal tuning fork armscomprises a plurality of vibrational portions having a first vibrationalportion including a generally tapered shape comprised of a plurality ofdifferent widths having a first width and a second width less than thefirst width, and a second vibrational portion including a third widthless than or equal to the first width, the first vibrational portion ofeach of the first and second quartz crystal tuning fork arms havingfirst and second opposite main surfaces each including a central linearportion; wherein the at least one groove comprises a groove formed inthe central linear portion of each of the first and second opposite mainsurfaces of the first vibrational portion of each of the first andsecond quartz crystal tuning fork arms so that a length of the grooveformed in the central linear portion of each of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms is within a range of0.45 mm to 1.25 mm and a width of the groove formed in the centrallinear portion of each of the first and second opposite main surfaces ofthe first vibrational portion of each of the first and second quartzcrystal tuning fork arms is within a range of 0.025 mm to 0.049 mm, afirst distance in the width direction of the groove measured from afirst outer edge of the groove to a first outer edge of thecorresponding one of the first and second quartz crystal tuning forkarms being defined by W₁ and a second distance in the width direction ofthe groove measured from a second outer edge opposite the first outeredge of the groove to a second outer edge opposite the first outer edgeof the corresponding one of the first and second quartz crystal tuningfork arms being defined by W₃, and so that each of the first distance W₁and the second distance W₃ is within a range of 0.003 mm to 0.012 mm;wherein the overall length of the quartz crystal tuning fork resonatoris within a range of 1.02 mm to 1.95 mm; wherein the second vibrationalportion of each of the first and second quartz crystal tuning fork armshas third and fourth opposite main surfaces; and wherein a metal filmfor adjusting an oscillation frequency of the quartz crystal tuning forkresonator is disposed on at least one of the third and fourth oppositemain surfaces of the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms.
 16. A quartz crystal unitaccording to claim 1; wherein the at least one mounting arm extends in acommon direction with the first and second quartz crystal tuning forkarms; and further comprising a case having a mounting portion and a lidfor covering an open end of the case; wherein the at least one mountingarm is mounted on the mounting portion of the case; wherein the lid isconnected to the case to cover the open end of the case; wherein alength L₁ of the quartz crystal tuning fork base is less than 0.5 mm;wherein each of the first and second quartz crystal tuning fork armscomprises a plurality of vibrational portions having a first vibrationalportion including a first width and a second vibrational portionincluding a second width greater than the first width, the firstvibrational portion of each of the first and second quartz crystaltuning fork arms having first and second opposite main surfaces; whereinthe at least one groove comprises a groove formed in at least one of thefirst and second opposite main surfaces of the first vibrational portionof each of the first and second quartz crystal tuning fork arms so thata width of the groove formed in the at least one of the first and secondopposite main surfaces of the first vibrational portion of each of thefirst and second quartz crystal tuning fork arms is less than aspaced-apart distance between the first and second quartz crystal tuningfork arms and less than 0.07 mm, and a distance in the width directionof the groove measured from an outer edge of the groove to an outer edgeof the corresponding one of the first and second quartz crystal tuningfork arms is less than 0.015 mm; wherein the second vibrational portionof each of the first and second quartz crystal tuning fork arms hasthird and fourth opposite main surfaces; and wherein a metal film foradjusting an oscillation frequency of the quartz crystal tuning forkresonator is disposed on at least one of the third and fourth oppositemain surfaces of the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms.
 17. A quartz crystal unitaccording to claim 16; wherein the at least one mounting arm has a firstarm portion including a first width and a second arm portion including asecond width greater than the first width; wherein the first arm portionof the at least one mounting arm is connected to the quartz crystaltuning fork base through a connecting portion; wherein the length of thequartz crystal tuning fork base is within a range of 0.015 mm to 0.49 mmand a width of the quartz crystal tuning fork base is within a range of0.15 mm to 0.53 mm; wherein the overall length of the quartz crystaltuning fork resonator is within a range of 1.02 mm to 1.95 mm; andwherein the second arm portion of the at least one mounting arm ismounted on the mounting portion of the case.
 18. A quartz crystaloscillator comprising: a plurality of capacitors; at least one resistor;and a quartz crystal unit comprised of a quartz crystal tuning forkresonator having a quartz crystal tuning fork shape including a quartzcrystal tuning fork base, and first and second quartz crystal tuningfork arms connected to the quartz crystal tuning fork base, each of thefirst and second quartz crystal tuning fork arms having a first mainsurface and a second main surface opposite the first main surface;wherein the quartz crystal tuning fork resonator of the quartz crystalunit is electrically connected to the capacitors and the at least oneresistor; wherein at least one groove is formed in at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork arms; wherein at least one mounting arm having awidth less than 0.45 mm protrudes from the quartz crystal tuning forkbase; and wherein an overall length of the quartz crystal tuning forkresonator is less than 2.1 mm.
 19. A quartz crystal oscillator accordingto claim 18; wherein the at least one mounting arm extends in a commondirection with the first and second quartz crystal tuning fork arms; andfurther comprising a case having a mounting portion and a lid forcovering an open end of the case; wherein the at least one mounting armis mounted on the mounting portion of the case; wherein the lid isconnected to the case to cover the open end of the case; and wherein awidth of the quartz crystal tuning fork base is less than 0.55 mm and alength L₁ of the quartz crystal tuning fork base is less than 0.5 mm.20. A quartz crystal oscillator according to claim 19; wherein the atleast one mounting arm has a first arm portion including a first widthless than 0.45 mm and a second arm portion including a second widthgreater than the first width and extends in a common direction with thefirst and second quartz crystal tuning fork arms outside the first andsecond quartz crystal tuning fork arms; wherein the first arm portion ofthe at least one mounting arm is connected to the quartz crystal tuningfork base through a connecting portion; wherein the length of the quartzcrystal tuning fork base is within a range of 0.015 mm to 0.49 mm andthe width of the quartz crystal tuning fork base is within a range of0.15 mm to 0.53 mm; wherein the overall length of the quartz crystaltuning fork resonator is within a range of 1.02 mm to 1.95 mm; andwherein the second arm portion of the at least one mounting arm ismounted on the mounting portion of the case.
 21. A quartz crystaloscillator according to claim 19; wherein the at least one mounting armcomprises first and second mounting arms each having a length L₃ withina range of 0.3 mm to 1.85 mm and a width less than 0.45 mm, each of thefirst and second mounting arms protruding from the quartz crystal tuningfork base and extending in a common direction with the first and secondquartz crystal tuning fork arms outside the first and second quartzcrystal tuning fork arms; wherein the first mounting arm is connected tothe quartz crystal tuning fork base through a first connecting portionand the second mounting arm is connected to the quartz crystal tuningfork base through a second connecting portion, each of the first andsecond connecting portions having a length L₂ within a range of 0.04 mmto 0.5 mm and a width less than 0.41 mm; wherein the case has first andsecond mounting portions; wherein the first mounting arm is mounted onthe first mounting portion of the case and the second mounting arm ismounted on the second mounting portion of the case; wherein each of thefirst and second quartz crystal tuning fork arms comprises a pluralityof vibrational portions having a first vibrational portion including afirst width and a second vibrational portion including a second widthgreater than the first width, the first vibrational portion of each ofthe first and second quartz crystal tuning fork arms having first andsecond opposite main surfaces; wherein the at least one groove comprisesa groove formed in each of the first and second opposite main surfacesof the first vibrational portion of each of the first and second quartzcrystal tuning fork arms so that a width of the groove formed in each ofthe first and second opposite main surfaces of the first vibrationalportion of each of the first and second quartz crystal tuning fork armsis less than 0.07 mm, a first distance in the width direction of thegroove measured from a first outer edge of the groove to a first outeredge of the corresponding one of the first and second quartz crystaltuning fork arms being defined by W₁ and a second distance in the widthdirection of the groove measured from a second outer edge opposite thefirst outer edge of the groove to a second outer edge opposite the firstouter edge of the corresponding one of the first and second quartzcrystal tuning fork arms being defined by W₃, and so that at least oneof the first distance W₁ and the second distance W₃ is less than 0.015mm; wherein the second vibrational portion of each of the first andsecond quartz crystal tuning fork arms has third and fourth oppositemain surfaces; and wherein a metal film for adjusting an oscillationfrequency of the quartz crystal tuning fork resonator is disposed on atleast one of the third and fourth opposite main surfaces of the secondvibrational portion of each of the first and second quartz crystaltuning fork arms.
 22. A quartz crystal oscillator according to claim 19;wherein the at least one mounting arm comprises first and secondmounting arms each having a length L₃ within a range of 0.3 mm to 1.85mm and a width less than 0.45 mm, each of the first and second mountingarms protruding from the quartz crystal tuning fork base and extendingin a common direction with the first and second quartz crystal tuningfork arms outside the first and second quartz crystal tuning fork arms;wherein the quartz crystal tuning fork base has two cut portions, and afirst base portion and a second base portion; wherein the two cutportions are formed between the first and second base portions of thequartz crystal tuning fork base, each of the first and second quartzcrystal tuning fork arms being connected to the first base portion ofthe quartz crystal tuning fork base; wherein the first mounting arm isconnected to the second base portion of the quartz crystal tuning forkbase through a first connecting portion and the second mounting arm isconnected to the second base portion of the quartz crystal tuning forkbase through a second connecting portion so that the second base portionof the quartz crystal tuning fork base and the first and secondconnecting portions have a U-shape or a concave shape with the first andsecond mounting arms, each of the first and second connecting portionshaving a length L₂ within a range of 0.04 mm to 0.5 mm and a width lessthan 0.41 mm; wherein the case has first and second mounting portions;wherein the first mounting arm is mounted on the first mounting portionof the case and the second mounting arm is mounted on the secondmounting portion of the case; wherein each of the first and secondquartz crystal tuning fork arms comprises a plurality of vibrationalportions having a first vibrational portion including a first width anda second vibrational portion including a second width greater than thefirst width, the first vibrational portion of each of the first andsecond quartz crystal tuning fork arms having first and second oppositemain surfaces each including a central linear portion; wherein the atleast one groove comprises a groove formed in the central linear portionof each of the first and second opposite main surfaces of the firstvibrational portion of each of the first and second quartz crystaltuning fork arms so that a width of the groove formed in the centrallinear portion of each of the first and second opposite main surfaces ofthe first vibrational portion of each of the first and second quartzcrystal tuning fork arms is less than 0.07 mm, a first distance in thewidth direction of the groove measured from a first outer edge of thegroove to a first outer edge of the corresponding one of the first andsecond quartz crystal tuning fork arms being defined by W₁ and a seconddistance in the width direction of the groove measured from a secondouter edge opposite the first outer edge of the groove to a second outeredge opposite the first outer edge of the corresponding one of the firstand second quartz crystal tuning fork arms being defined by W₃, and sothat each of the first distance W₁ and the second distance W₃ is lessthan 0.015 mm; wherein the second vibrational portion of each of thefirst and second quartz crystal tuning fork arms has third and fourthopposite main surfaces; and wherein a metal film for adjusting anoscillation frequency of the quartz crystal tuning fork resonator isdisposed on at least one of the third and fourth opposite main surfacesof the second vibrational portion of each of the first and second quartzcrystal tuning fork arms.
 23. A quartz crystal oscillator according toclaim 19; wherein the at least one mounting arm comprises first andsecond mounting arms each having a length L₃ within a range of 0.3 mm to1.85 mm and a width less than 0.45 mm, each of the first and secondmounting arms protruding from the quartz crystal tuning fork base andextending in a common direction with the first and second quartz crystaltuning fork arms outside the first and second quartz crystal tuning forkarms; wherein the quartz crystal tuning fork base has two cut portions,and a first base portion and a second base portion; wherein the two cutportions are formed between the first and second base portions of thequartz crystal tuning fork base, each of the first and second quartzcrystal tuning fork arms being connected to the first base portion ofthe quartz crystal tuning fork base; wherein the first mounting arm isconnected to the second base portion of the quartz crystal tuning forkbase through a first connecting portion and the second mounting arm isconnected to the second base portion of the quartz crystal tuning forkbase through a second connecting portion, each of the first and secondconnecting portions having a length L₂ within a range of 0.04 mm to 0.5mm and a width less than 0.41 mm; wherein the case has first and secondmounting portions; wherein the first mounting arm is mounted on thefirst mounting portion of the case and the second mounting arm ismounted on the second mounting portion of the case; wherein each of thefirst and second quartz crystal tuning fork arms comprises a pluralityof different widths; wherein each of the first and second main surfacesof each of the first and second quartz crystal tuning fork arms has acentral linear portion; wherein the at least one groove comprises agroove formed in the central linear portion of each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork arms so that a width of the groove formed in the centrallinear portion of each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork arms is less than 0.07mm, a first distance in the width direction of the groove measured froma first outer edge of the groove to a first outer edge of thecorresponding one of the first and second quartz crystal tuning forkarms being defined by W₁ and a second distance in the width direction ofthe groove measured from a second outer edge opposite the first outeredge of the groove to a second outer edge opposite the first outer edgeof the corresponding one of the first and second quartz crystal tuningfork arms being defined by W₃, and so that each of the first distance W₁and the second distance W₃ is less than 0.015 mm; and wherein theoverall length of the quartz crystal tuning fork resonator is within arange of 1.02 mm to 1.95 mm.
 24. An electronic apparatus comprising: adisplay portion; and a quartz crystal oscillator having a plurality ofcapacitors, at least one resistor, and a quartz crystal unit comprisedof a quartz crystal tuning fork resonator having a quartz crystal tuningfork shape including a quartz crystal tuning fork base, and first andsecond quartz crystal tuning fork arms connected to the quartz crystaltuning fork base, each of the first and second quartz crystal tuningfork arms having a first main surface and a second main surface oppositethe first main surface; wherein the quartz crystal tuning fork resonatorof the quartz crystal unit is electrically connected to the capacitorsand the at least one resistor; wherein at least one groove is formed inat least one of the first and second main surfaces of each of the firstand second quartz crystal tuning fork arms; wherein at least onemounting arm having a width less than 0.45 mm protrudes from the quartzcrystal tuning fork base; wherein an overall length of the quartzcrystal tuning fork resonator is less than 2.1 mm; and wherein an outputsignal of the quartz crystal oscillator comprising the quartz crystaltuning fork resonator is a clock signal for use in operation of theelectronic apparatus to display time information at the display portionthereof.
 25. An electronic apparatus according to claim 24; wherein theat least one mounting arm has a first arm portion including a firstwidth less than 0.45 mm and a second arm portion including a secondwidth greater than the first width and extends in a common directionwith the first and second quartz crystal tuning fork arms; wherein thefirst arm portion of the at least one mounting arm is connected to thequartz crystal tuning fork base through a connecting portion having awidth less than 0.41 mm and a length within a range of 0.04 mm to 0.5mm; wherein the quartz crystal tuning fork base has a length less than0.5 mm and a width within a range of 0.15 mm to 0.53 mm; wherein theoverall length of the quartz crystal tuning fork resonator is within arange of 1.02 mm to 1.95 mm; and further comprising a case having amounting portion and a lid for covering an open end of the case; whereinthe second arm portion of the at least one mounting arm is mounted onthe mounting portion of the case; wherein the lid is connected to thecase to cover the open end of the case; wherein a first electrode isdisposed on a surface of the at least one groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork arms; wherein a second electrode isdisposed on a surface of the mounting portion of the case; wherein athird electrode is disposed on a surface of the connecting portion;wherein a fourth electrode is disposed on a surface of each of the firstand second arm portions of the at least one mounting arm; and whereinthe first electrode disposed on the surface of the at least one grooveformed in the at least one of the first and second main surfaces of oneof the first and second quartz crystal tuning fork arms is connected tothe second electrode disposed on the surface of the mounting portion ofthe case through the third electrode disposed on the surface of theconnecting portion and the fourth electrode disposed on the surface ofeach of the first and second arm portions of the at least one mountingarm.
 26. An electronic apparatus according to claim 25; wherein thequartz crystal tuning fork base has a first base portion including afirst width, a second base portion including a second width and a thirdbase portion including a third width less than each of the first andsecond widths, the third base portion being located between the firstand second base portions and the first base portion being connected tothe second base portion through the third base portion, each of thefirst and second quartz crystal tuning fork arms being connected to thefirst base portion of the quartz crystal tuning fork base; wherein theat least one mounting arm comprises a plurality of mounting arms havingfirst and second mounting arms, each of the first and second mountingarms extending in a common direction with the first and second quartzcrystal tuning fork arms outside the first and second quartz crystaltuning fork arms and having first, second, third, fourth and fifth armportions, each of the first, third and fifth arm portions extendingsubstantially parallel to the first and second quartz crystal tuningfork arms, the first arm portion being connected to the third armportion through the second arm portion extending not parallel to thefirst and second quartz crystal tuning fork arms, and the third armportion being connected to the fifth arm portion through the fourth armportion extending not parallel to the first and second quartz crystaltuning fork arms; wherein the first arm portion of the first mountingarm is connected to the second base portion of the quartz crystal tuningfork base through a first connecting portion and the first arm portionof the second mounting arm is connected to the second base portion ofthe quartz crystal tuning fork base through a second connecting portionso that the second base portion of the quartz crystal tuning fork baseand the first and second connecting portions have a U-shape or a concaveshape with the first arm portions of the first and second mounting arms;wherein the case has first and second mounting portions; wherein thefifth arm portion of the first mounting arm is mounted on the firstmounting portion of the case and the fifth arm portion of the secondmounting arm is mounted on the second mounting portion of the case; andwherein each of the first and second mounting arms has a width less than0.45 mm and a length within a range of 0.3 mm to 1.85 mm.
 27. Anelectronic apparatus according to claim 24; wherein the at least onemounting arm has a width less than 0.45 mm and is connected to thequartz crystal tuning fork base having a length L₁ and a width within arange of 0.15 mm to 0.53 mm through a connecting portion having a lengthL₂ and a width less than 0.41 mm; wherein a value of L₁−L₂ is within arange of 0.1 mm to 0.32 mm; and further comprising a case having amounting portion and a lid for covering an open end of the case; whereinthe at least one mounting arm is mounted on the mounting portion of thecase; and wherein the lid is connected to the case to cover the open endof the case.
 28. An electronic apparatus according to claim 27; whereinthe at least one mounting arm comprises first and second mounting armseach having a length L₃ within a range of 0.3 mm to 1.85 mm and a widthless than 0.45 mm, each of the first and second mounting arms protrudingfrom the quartz crystal tuning fork base and extending in a commondirection with the first and second quartz crystal tuning fork armsoutside the first and second quartz crystal tuning fork arms; whereinthe quartz crystal tuning fork base has two cut portions, and a firstbase portion and a second base portion; wherein the two cut portions areformed between the first and second base portions of the quartz crystaltuning fork base, each of the first and second quartz crystal tuningfork arms being connected to the first base portion of the quartzcrystal tuning fork base; wherein the first mounting arm is connected tothe second base portion of the quartz crystal tuning fork base through afirst connecting portion and the second mounting arm is connected to thesecond base portion of the quartz crystal tuning fork base through asecond connecting portion, each of the first and second connectingportions having a length L₂ within a range of 0.04 mm to 0.5 mm and awidth less than 0.41 mm; wherein the case has first and second mountingportions; wherein the first mounting arm is mounted on the firstmounting portion of the case and the second mounting arm is mounted onthe second mounting portion of the case; wherein each of the first andsecond quartz crystal tuning fork arms comprises a plurality ofdifferent widths, each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork arms having a centrallinear portion; wherein the at least one groove comprises a grooveformed in the central linear portion of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forkarms so that a width of the groove formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork arms is less than 0.07 mm, a firstdistance in the width direction of the groove measured from a firstouter edge of the groove to a first outer edge of the corresponding oneof the first and second quartz crystal tuning fork arms being defined byW₁ and a second distance in the width direction of the groove measuredfrom a second outer edge opposite the first outer edge of the groove toa second outer edge opposite the first outer edge of the correspondingone of the first and second quartz crystal tuning fork arms beingdefined by W₃, and so that each of the first distance W₁ and the seconddistance W₃ is less than 0.015 mm.
 29. An electronic apparatus accordingto claim 28; wherein the width of the groove formed in the centrallinear portion of each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork arms is within a rangeof 0.025 mm to 0.049 mm; wherein each of the first distance W₁ and thesecond distance W₃ is within a range of 0.003 mm to 0.012 mm; andwherein the overall length of the quartz crystal tuning fork resonatoris within a range of 1.02 mm to 1.95 mm.